Osu! is a rhythm game released on September 16th, 2007 for Microsoft Windows (later to be made available on macOS, Linux, Android, and iOS), made by Dean "Peppy" Herbert. The game features 4 main gamemodes inspired by various other games and has attracted over 17+ million players worldwide.
The 4 gamemodes:
Osu!standard (AKA Osu!, Osu!std)
The primary and most popular gamemode in Osu!, which is inspired by the games "Osu! Tatakae! Ouendan" and "Elite Beat Agents". The gameplay of this mode features 3 mechanics, the hit circle (which you simply tap), the slider (which you hold and move with the path it's set on) and the spinner (which you rapidly spin your cursor around the middle of the screen).
Top player (as of when this was written) : WhiteCat
Taiko is a game mode which consists of tapping 2 notes to the beat on a drum-like interface, inspired by the Taiko no Tatsujin series.
Top player: nameless_ll
Osu!catch (AKA Osu!ctb [catch the beat])
Catch is a gamemode which consists of controlling a small character at the bottom of the screen to collect falling fruit to the beat.
Top player: Motion
Mania is a gamemode which consists of hitting falling notes to the beat, similar to most VSRGs (vertical scrolling rhythm games). The number of notes on the screen at once can range from 1-10 notes, with 4 notes and 7 notes being the most popular among players.
Top player: Jakads