Tennis has a very idiosyncratic scoring system, and no one is sure why.
Most sports count points by ones. But in a game of tennis, the players don't start at zero, they start at "love". If one player then scores, they have 15. The next score is 30, so you would probably expect the following one to be 45. But no, it's 40. If the two players are tied at 40-40, that's "deuce" (pronounced like "juice", which could be confusing!) The player who wins the next point has "advantage". If they win the following one, they win the game. If their opponent wins the point after advantage, then the score returns to deuce.
The number of games won in a set, or sets won in a match, are numbered in the more "normal" way of 1, 2, 3... The first player to six games wins the set, if there is a two point difference. The first player to two sets out of a possible three (women's singles) or three sets out of a possible five (men's), wins.
AELTC Edward Whitaker