A yaku「役」 is a certain pattern in a mahjong hand, or a special condition under which a win is declared. Many yaku are pattern-based yaku comparable to "poker hands". Unlike poker, yaku types do not supercede each other. Instead, they are the main factor to determine hand values. Players must finish hands before others do; and each yaku has specific values attached to them to determine payment amounts.
The yaku and their values are essential for scoring. The game rules define lots of different yaku, worth a different amount of han「飜」 based on their difficulty or pre-assigned value. A player can incorporate several different yaku in the same hand and accumulate their han values for high-scoring hands. For additional scoring, the game also features dora. However, possession of dora are not considered as yaku, even though they provide han.
In order to win any hand in this game, a player requires at least one yaku. A hand having no yaku may not win, even if it has multiple dora. Declaring a win on a yakuless hand may result in chombo. So, as an early part of the game's learning process, it is essential to learn the different yaku listed here and eventually their han values.
The most important yaku to learn is riichi, since it is very common and a very easy yaku to achieve. A new player may find it easiest to avoid opening their hand and simply aim for riichi every time; no other yaku is required to win the hand. However, this strategy is far too simple for serious play and an experienced player should generally aim for a high-scoring yaku or combination of yaku from the beginning of the hand.
This hand has a complete sequence of 1 through 9 of a single suit. As a note, the sequence of 1-9 are actually three groups of sequences numbered 123, 456, and 789.
The hand includes three groups of triplets (or closed quads) that have been formed without calling any tiles. The fourth group can be an open triplet or sequence.
The hand is composed of nothing but all terminals and honors. † This hand may be considered as 4 han, because it is impossible to score this hand without either chii toitsu or toi toi.
The hand contains two sets of 3 dragon tiles and a pair of the third dragon tiles. † This hand may be considered as 4 han, because it is impossible to score this hand without two sets of yakuhai, from the two sets of dragons.
This hand is composed entirely of tiles from only one of the three suits. It is the only yaku set at 6 han, where the number drops to 5 han when opened.
This hand has one of each of the 13 different terminal and honor tiles plus one extra terminal or honour tile. Some rules may allow double yakuman for a 13-wait set.
This hand is composed of four groups of closed triplets. When this hand has a shanpon pattern and the win is via ron, then it would not be counted as such; only as the lesser toitoi with sanankou.
The non-dealer hand is a winning hand with the first tile draw.
Special case
This yaku does not specifically deal with a player's hand, but rather the player's discards. In addition, the hand may or may not be at tenpai upon scoring. By default, this hand is set to mangan.
The above list is generally considered as the "standard yaku", including the yakuman. However, the game offers an even larger array of tile patterns. Various house rules may opt to use some of these yaku on their own.
or 
Agari: 
Agari: 