Traditionally, tennis is played between two people in a singles match, or two pairs in a doubles match.
Singles involves two players competing against each other, usually two men or two women, although games between a man and a woman may be played on an informal basis or as exhibitions.
Doubles is played by two teams of two players each, most often all-male or all-female. It utilizes a wider court than singles matches: it includes the area in the alley (tramlines, in British terminology), whereas singles does not. The two players on the receiving side change positions after each point played (one at the net and the other near the baseline, preparing to return serve).
Mixed doubles is played the same as doubles, but with one man and one woman per team. This form of tennis is rare in the professional game because the men's and women's tours are organised separately (by the ATP and WTA, respectively). However, all four Grand Slam tournaments hold a mixed doubles competition, alongside the men's and women's doubles, featuring many of the same players. There is also an annual mixed tournament for national teams, the Hopman Cup, which includes mixed doubles matches. Additionally, there have been mixed doubles events at the Summer Olympics on various occasions (In 1900, from 1912 until 1920 and again since 2012).
While players are gradually less competitive in singles by their late 20s and early 30s, they can still continue competitively in doubles and mixed doubles (as instanced by Martina Navratilova and John McEnroe, who won doubles titles in their 40s).
When three players are available, modified rules can accommodate the mismatch so that the single player does not have to be significantly better than the double team. The single player hits into a doubles court while the side with two players hits into a singles court.
An informal and unsanctioned form of tennis, this is played with similar rules to Canadian doubles, only in this version, players rotate court position after each game. As such, each player plays doubles and singles over the course of a match, with the singles player always serving. Scoring styles vary, but one popular method is to assign a value of 2 points to each game, with the server taking both points if he or she holds serve, and the doubles team each taking one if they break. Throughout the United Kingdom (particularly England) and Australia this format is usually known as "American doubles", whereas in South Africa you would call it "American singles", or cut-throat tennis. It is also found in the Caribbean 
A game played between three players. A normal tennis game takes place between two of the three contestants. Players are awarded 5 points for a game win and the loser is awarded points based on the score achieved: 3 for deuce, 2 for 30 and 1 for 15. The winner remains in. The player replacing the loser gets to choose who serves. The first to 50 wins. Scoring is calculated continuously, so if a player is currently on 49 points at the start of a game they only have to win one point for the game to end. There is a variation invented in 2005, called "mini-Jordache", where the first person to 25 points wins.
Played in both singles and doubles forms by people in wheelchairs. The main difference is that the ball may bounce twice before it is hit, the second bounce may even be outside the court. All four Grand Slam tournaments include wheelchair tennis.
There is an evolution in tennis training that employs the use of low compression balls and in some cases modified court sizes. Organizations around the world have begun to use lower compression balls and modified court sizes as a way to reach out to younger tennis players interested in tennis. The use of low compression balls and modified court sizes is meant to ease the process into becoming a competitive or amateur tennis player. The low compression balls are colored differently to indicate the level of compression. Young players and beginners are likely to find the game easier to learn because the balls do not bounce as high or travel as fast as "normal" balls. The modified smaller courts make covering the court, or reaching the opponents shot, easier as well.