Zendo is, as noted above, a board game of logic and deduction. However, things have changed a bit. In 1996, Kristin and Andrew Looney shut down Icehouse Games (the pyramids were becoming too expensive to make), and started Looney Labs, with the intent of creating a card game. They succeed with the popular Fluxx game(s), and eventually started making games with the Icehouse Pyramids again in 2006. Zendo was re-released in 2017.
The core game is the same as the original, but there were changes. First, the game is stripped of all references to students, masters, and koans. We now have players, a moderator, and rules. There are still three pieces, but instead of small, medium, and large, we have pyramid, wedge, and block. Instead of five colors, we have just three (red, blue, and yellow). And there are no pips on any pieces. This does not hurt game-play at all.
Zendo has an additional rule that was not noted above, but it has not changed between editions; when a player makes a construction, they may choose to have all players guess if it will be declared correct or incorrect by the moderator. All players who guess correctly get a small green cube (originally called a 'guessing stone'); and a player must spend one of these cubes in order to make a guess at the rule. This is an okay mechanic, and keeps people from getting bogged down on making random guesses early on in the game; however, when playing with experienced players this mechanic is often dropped with no ill effects.
The new release also contains a deck of cards that have rules on them leveled by difficulty. This is a very useful brake on the moderator's inventiveness, and I recommend them for new players.