Teeing Ground
Order of play
Falling off tee

Playing the Ball
Unplayable
Wrong, Substitute
Lifting, dropping
Moved, deflected

Provisional, Lost, Out of bounds

Putting Green
Flagstick
Marking, lifting
Stymie

Hazards, Penalty Areas
Water hazards
Lateral water hazards

Abnormal Conditions
GUR
Casual water, Temporary water
Hole, cast, or runway

Obstructions,
Loose impediments

Play the ball as it lies. Play the course as you find it. And if you can't do either, do what is fair

Lifting and Dropping
Through the green was first defined in 1899, as being all parts of the course except hazards and the putting green. The teeing ground was added to the definition in 1933.

Apart from taking a ball out of a hazard, lifting was initially allowed only for balls touching, then within six inches of each other from 1775.
The first 'procedure' for dropping a ball came in 1754: throwing it behind a water hazard 'six yards at least'. Apart from 1754 and HCEG 1809, all codes up to 1888 allowed a ball to be teed behind if it was in water, but the ball was to be dropped in other instances.

R &A 1858 stipulated a drop on a line from the hole behind the hazard, establishing the principle used ever since.

R&A 1891 in stroke play allowed a ball to be teed for lost ball and a ball 'lifted out of any difficulty', (in match play both these occurrences were loss of hole).

The first mention of placing, rather than dropping, a ball on the putting green came in 1902.

The method of dropping a ball had a few early variants:
1754 throw it at least six yards; 1776 Edinburgh Burgess throw it over your head; 1809 HCEG, 1830 Montrose, 1839 Royal Perth and 1812 R&A, face the hole, and drop over the head; and the latter to be adopted over the shoulder from Perth 1825 and Blackheath 1828.
When the 1899 rules came into force, the procedure was well detailed: behind the hazard, face the hole, stand erect and drop it from your head on a line from the hole.
In 1908 the new procedure of dropping over the shoulder introduced. It lasted until 1984, when the method of dropping at arm's length was introduced.
2019 A ball to be dropped is now done from knee height or lower.

Re-dropping was required if the ball:
1899 rolls into a hazard.
1933 rolls nearer the hole.
1950 (R&A) goes out of bounds, into a hazard or casual water.
1954 rolls out of a hazard.
1960 rolls more than 2 club lengths.
1964 strikes the player, play as it lies. Re-drop required from 1976
1980 rolls onto a putting green.
1984 rolls back into the condition from which relief is being taken.
1996 not nearer hole than point where last crossed margin of WH.

1952 One re-drop before placing if the ground is such that it prevents a correct drop.
1972 after re-drop, ball to be placed at point ('spot' from 1984) where last dropped.

Lifting for ID
1908 A player can lift anywhere for identification in the presence of another player.
1956 ball may not be lifted for identification in a hazard.
2008 Ball again may be lifted anywhere for identification

R&A 1891 sees the first mention of placing a ball on the putting green, no doubt at the behest of greenkeepers who around this time started keeping the area around the hole well-tended.

Marking
Initially, there was no requirement for a ball that was to be lifted and replaced to be marked at all. A ball had to be marked when lifting from the putting green from 1976, and marked if it was to be replaced anywhere else on the course from 1984.
More details on marking on the green here.

Wrong ball
No mention was made of a wrong ball in any code until the 1800s.
1828 Blackheath - if a player plays opponent's ball, the opponent plays as it lies, no stroke penalty.
1815 Aberdeen - if a player plays a wrong ball, opponent can have stroke or replay ball.
1812 R&A had a simple sentence: If the player strikes his adversary's ball with his club, the player loses the hole.

The featherie ball did not fly very far, so the issue of playing a ball from outside the match probably did not arise very often. Also the balls were far too expensive to leave behind on the course, so a stray ball was a rare thing.
After the introduction of the guttie, which flew further, and the increasing popularity of golf, the possibility became real enough for the R&A to expand on a rule in 1858. Penalty for playing a wrong ball was loss of hole, however if the balls were inadvertently exchanged then there was no penalty to either side and the ball were played out thus exchanged.

1891 R&A. Penalty for playing an opponent's ball changed to 1 stroke unless this was due to wrong information, then there was no penalty and the player replaced his ball.
Playing a ball from outside the match if discovered before teeing off on the next hole was loss of hole, otherwise no penalty.

1899 Penalty back to loss of hole. Stroke play, no penalty if corrected.

1902 If a player played a ball from outside the match, there was no penalty if opponent informed before playing. Otherwise loss of hole.

1908 In stroke play no penalty for playing one stroke with a wrong ball, but DQ for two successive strokes; no penalty if played from hazard.

1933 Stroke play penalty reduced to 2 strokes, but applies to the first stroke with the wrong ball.

1950 R&A. Reduction of penalty to one stroke if the player immediately informed his opponent, otherwise loss of hole.  if player plays opponent's ball and then opponent plays a wrong ball - no penalty. For a ball outside the match 1 stroke -- treated the same.
Stroke play: 1 stroke. No penalty if played from within a hazard.

1952. Playing a wrong ball is loss of hole, or 2 strokes in stroke play.

1954, added that strokes played with a wrong ball do not count in player's score.

2008 As identification is now allowed in a hazard, the penalty for playing a wrong ball from a hazard is reinstated.

The Wrong Rule, 1964-71
From 1964, in addition to a wrong ball, there was the possibility of playing under a wrong rule.
If a player proceeded under a rule which did not cover the case, the penalty was loss of hole, or 2 strokes, then proceed under the correct rule. Strokes played don't count.
1972 this rule was replaced by 'playing from a wrong place'.

Unplayable
An unplayable ball was not contemplated by the early rules - either you played it as it lay or you lost the hole, unless the ball was in water.  This rule was, of course, unworkable for stroke play where it was necessary to allow the player to continue the round and record a score on each hole.

Edinburgh Burgess in 1807 introduced a rule for medal play allowing a player to lift a ball at any time and drop it over his shoulder, penalty one stroke. The same rule was applied by the Honourable Company in1809, Thistle 1824 and Perth 1825.

Burntisland 1828 introduced a novel version of the unplayable ball: if the player believes he cannot play the ball, his adversary may try to do so. If the adversary either fails or declines to do so, the player can then proceed to drop the ball.
R&A, 1851 With the consent of one's adversary, a player could lift and drop behind the place for 1 penalty stroke. If the adversary disagreed, he could take two strokes at the ball to make it playable. If he succeeded then the 2 strokes were added to the players score and he played on. If not then the player proceeded with the drop.

R&A 1858 Match play, play the ball as it lies or lose the hole, except if the ball is on an obstruction or in water in which case no penalty but the ball must be played with an iron club. Stroke play, the ball may be lifted from anywhere and teed behind the place; 2 penalty strokes.

Liverpool (Hoylake; now Royal Liverpool) 1870: An opponent was allowed three strokes in which to make the ball playable, if he succeeded, the player incurs the additional strokes; if not, the opponent added them to HIS score!

1902. Stroke play, 2 penalty strokes and the player shall tee a ball behind the spot.

1920: Ball now can be 'deemed' unplayable anywhere on the course; penalty stroke and distance in match play, stroke and distance or tee behind the place for 2 strokes in stroke play.

Although a ball could be declared unplayable anywhere at this time, if a player's ball was in a water hazard, by following the water hazard Rule he could get back into play for one penalty stroke instead of two in stroke play (or loss of hole in match play).

The blueprint for the modern unplayable rule came from:
1941 USGA. The player is the sole judge as to whether his ball is unplayable. It may be declared unplayable at any place on the course, except in a water hazard or in casual water.
1947 the USGA said a ball could be declared anywhere on the course. In stroke play a ball may be lifted from any place except a water hazard, penalty one stroke.

1950. Unplayable is defined: 'if the player consider he cannot make a stroke at it and dislodge it into a playable position'.
1952 definition dropped.

Also in 1950 penalties reduced to distance only for lost, out of bounds and unplayable. Relief either distance only or within 2 club lengths, 1 penalty stroke. Provisional ball for a ball unplayable not allowed.
For more on provisional ball, see here.

1952 Lost, Unplayable, OOB all under same rule and penalties. Player is sole judge whether his ball is unplayable, and it can be declared Unplayable anywhere. Options are stroke and distance or 2 strokes and drop back on a line. Provisional ball allowed.
1960 USGA. reduced penalty to 1 stroke and removed Provisional option.
1964 option added to drop within 2-club lengths of ball, 2 penalty strokes.
1968 R&A. penalty reduced to 1 stroke, no provisional. Ball cannot now be declared unplayable in a water hazard.

1984 became a rule in its own right
2004 the old 1920 term 'deem' returns in place of 'declare'.
2019 A ball deemed unplayable in a bunker may be dropped outside the bunker. Two stroke penalty.

Moved, deflected
Ball deflected by an outside agency - more or less unchanged since 1744.

1891 R&A. 'Moved' defined, as today.

1908 A ball moved by another - player can choose to play as it lies or replace (MP); must be replaced in SP.
If accidentally moved, 1 penalty stroke, play the ball as it lies.
Ball moved in search - no penalty.

Playing
Ball moved by player: 1 ps and play as it lies; must be replaced from 1976.

Ball moves after address: play it as it lies, from 1988 ball must be replaced.

1775 Gentlemen Golfers. Ball deflected by adversary or his caddie, 1 penalty stroke to the adversary.

1812 St Andrews. Ball strikes adversary/caddie, adversary loses hole. Strikes own cady, loss of hole.

1829 St Andrews. add equipment; and if strikes self, loss of hole.

1858 R&A. Double hit: lose hole in match play, one stroke in stroke play.
1899 R&A.Double hit, one stroke penalty in both forms of play
2019: Double hit, no penalty. Accidentally moving a ball in searching or on the putting green, no penalty. Ball deflects off player or his equipment, no penalty.

In Play
1891 all balls must be holed out in Stroke Play.

1899 ball played out of turn may be recalled. R&A 1875 recall on tee only.

1899 ball must not be pushed scraped or spooned.
1899 If a player plays on putting green when another ball in motion, 1 penalty stroke.

1968 Stance defined.

1950 'Undue delay' introduced, penalty disqualification. 1952 DQ for undue delay reduced to 2ps

1960 Artificial devices and distance-measuring devices banned. 2008 Distance measuring devices allowed under Local Rule, and allowed fully in 2019.

Substitution

1744 From the start, there was no provision for substituting a ball: rule 3. In Rule 8, Substitution was allowed only for a ball lost (in whatever way). In what is now a water hazard, a player was allowed to take relief but with the same ball.
The situation was obviously the same in St Andrews 1754.
Exceptions in 18th century were Bruntsfield 1773, who allowed a change of ball by agreement with an opponent and also to replace a ball taken by a dog.
Aberdeen 1783 also allowed for a ball taken by a dog, and also allowed a substitute ball for one lost in water.
A lot of rules codes played lost ball=lost hole in match play, so the issue of a substitute ball did not arise, but these places had a separate rule for stroke play.

This situation continued uniformly throughout the codes of the 19th century, until R&A 1858 which allowed a change of ball from a water hazard and for a broken ball (this appears around the time the more fragile gutta percha ball was becoming popular).

Isle of Wight 1886 allowed a substitute ball for broken/damaged ball, a ball moved by an outside agency, if played by an opponent, in water, or a water hazard, OOB, and lost.

R&A 1888 also allowed for substitution for a ball in water, moved by an OA, and broken/damaged - added with opponent's consent in 1891.
1899 water hazard included.
1920 Unplayable ball defined and included in substitution; now no distinction between match and stroke play.
1950 substitution allowed from GUR - 1952 reversed, now only for ball lost in GUR or casual water.
1980 substitution of a ball after discontinued play allowed.
1984 substitution allowed if ball is not immediately recoverable for ball moved by another player or outside agency.
1992 expanded to include balls lost in immovable obstructions and GUR.
2000 substituted ball gets own sub-section; substitute ball becomes ball in play whether permitted or not.
2004 substituted ball defined. Also see lost ball.
2019 Substitute ball allowed when taking any form of relief. 2023 Penalty for incorrectly substituting ball reduced from two strokes to one.