Law 32 (Caught)
1. Out Caught
The striker is out Caught if a ball delivered by the bowler, not being a No ball, touches his bat without having previously been in contact with any member of the fielding side and is subsequently held by a fielder as a fair catch before it touches the ground.

2. Caught to take precedence
If the criteria of 1 above are met and the striker is not out Bowled, then he is out Caught, even though a decision against either batsman for another method of dismissal would be justified. Runs completed by the batsmen before the completion of the catch will not be scored. Note also Laws 21.6 (Winning hit or extras) and 42.17(b) (Penalty runs).

3. A fair catch
A catch shall be considered to have been fairly made if
(a) throughout the act of making the catch
(i) any fielder in contact with the ball is within the field of play. See 4 below.
(ii) the ball is at no time in contact with any object grounded beyond the boundary.

The act of making the catch shall start from the time when a fielder first handles the ball and shall end when a fielder obtains complete control both over the ball and over his own movement.

(b) the ball is hugged to the body of the catcher or accidentally lodges in his clothing or, in the case of the wicket-keeper, in his pads. However, it is not a fair catch if the ball lodges in a protective helmet worn by a fielder. See Law 23 (Dead ball).

(c) the ball does not touch the ground, even though the hand holding it does so in effecting the catch.

(d) a fielder catches the ball after it has been lawfully struck more than once by the striker, but only if the ball has not touched the ground since first being struck.

(e) a fielder catches the ball after it has touched an umpire, another fielder or the other batsman. However, it is not a fair catch if the ball has touched a protective helmet worn by a fielder, although the ball remains in play.

(f) a fielder catches the ball in the air after it has crossed the boundary provided that
(i) he has no part of his person touching, or grounded beyond, the boundary at any time when he is in contact with the ball.
(ii) the ball has not been grounded beyond the boundary.
See Law 19.3 (Scoring a boundary).

(g) the ball is caught off an obstruction within the boundary, provided it has not previously been decided to regard the obstruction as a boundary.

4. Fielder within the field of play
(a) A fielder is not within the field of play if he touches the boundary or has any part of his person grounded beyond the boundary. See Law 19.3 (Scoring a boundary).

(b) 6 runs shall be scored if a fielder
(i) has any part of his person touching, or grounded beyond, the boundary when he catches the ball.
(ii) catches the ball and subsequently touches the boundary or grounds some part of his person over the boundary while carrying the ball but before completing the catch.

See Laws 19.3 (Scoring a boundary) and 19.4 (Runs allowed for boundaries).

5. No runs to be scored
If the striker is dismissed Caught, runs from that delivery completed by the batsmen before the completion of the catch shall not be scored, but any penalties awarded to either side when the ball is dead, if applicable, will stand. Law 18.12(a) (Batsman returning to wicket he has left) shall apply from the instant of the catch.