What does !? mean in chess?

It is an annotator saying the move is interesting and probably not entirely sound: worth playing, worth a look, not something they would have chosen themselves. Its mirror image is ?!, a move the annotator does not like but cannot refute. Both are opinions written after the game, and an engine will happily overturn either of them.

What does ± mean in a chess book?

That White has a clear advantage, though not a forced win. The mirror is ∓ for Black. A slight edge is written ⩲ and ⩱, a winning position is +- and -+, and a level one is =. None of these appear during a game; they are an annotator's summary of the position after the move they are attached to.

Chess notation symbols explained

There are three separate pieces of information in exd5!? and only one of them is a fact. A pawn on the e-file captured on d5: that happened, and it is not open to debate. The x tells you something came off the board. The !? is one annotator’s opinion that the capture was interesting and possibly unsound, and you are free to disagree with it.

Sort the symbols by that test, fact or opinion, and the whole list takes ten minutes.

Marks that are part of the move

x a capture: Nxf3, or exd5 for a pawn, which shows its file instead of a letter. There is a page on what x means.
+ check: Qh5+, O-O-O+. It always comes last. See what + means.
# checkmate, and the end of the game: Qxf7#. Older books print ++ or ‡ instead. See what # means.
O-O castling on the king’s side, O-O-O on the queen’s side, both written with zeros in the FIDE laws. See what O-O means.
=Q a promotion: e8=Q, gxh8=N. Some books write e8Q or e8(Q).
e.p. an en passant capture: exd6 e.p., and the label is optional. See what e.p. means.
1... three dots in front of a move mean the move is Black’s.

None of those is a judgement. Two people writing down the same game should produce the same characters, which is the entire point of having a standard.

Marks that grade the move

! good, !! brilliant, ? a mistake, ?? a blunder, !? interesting, ?! dubious. The Chess Informant series standardised the set and every publisher followed.

The double-barrelled pair are the ones worth understanding. !? roughly means “I would not have played it, but I like it”. ?! means “I would not have played it, and I do not like it”. Neither is a verdict, and a strong engine cheerfully overturns both.

Marks that describe the position

= the position is level. ∞ unclear, the annotator’s shrug. ± White is clearly better, ∓ Black is clearly better, and the smaller edges are ⩲ and ⩱. Winning is +- for White and -+ for Black.

Note that = does three jobs and context sorts them out. In e8=Q it introduces a promoted piece. Standing alone after a move it means equality. In brackets on a scoresheet, (=), it records a draw offer (Art. 8.1.4).

Marks that end the game

1-0 White won. 0-1 Black won. ½-½ a draw, typed as 1/2-1/2 in a PGN file, since those are plain text. * means unfinished or unknown, which is what a live broadcast shows while the players are still sitting there.

Those go at the foot of a scoresheet and at the end of a game score, and they say nothing about how it happened: 1-0 covers a checkmate, a resignation and a lost flag equally.

If you want to watch the grading symbols being used in anger rather than defined, the solutions to the mate in two puzzles are written in exactly this shorthand, and reading a few dozen of them is faster than memorising any list.