Platform:
Platform games are a sub genre of action games, they involve getting an avatar to the end of the level by jumping between suspended platforms, dodging obstacles and defeating or avoiding enemies. The thing that brings these games together is commonly a jump button. Platform games are not a pure genre, frequently having elements of other genres, like adventure, RPG, shooter and puzzle.
Puzzle:
Puzzle games are made to focus on logical and mental challenges, sometimes with some sort of pressure like a timer or certain amount of tries. They normally involve colours, symbols, or shapes. Likely involving the player trying to put them in a certain position. There are also different sub-genres for puzzle games: Action Puzzle (Does Not Commute), Hidden Object Game (CSI: Hidden Crimes), Reveal The Picture (Guess The Picture), Physics Game (Cut The Rope), Tile-Matching (Threes!) and Traditional Puzzle (Mahjong Solitaire).
Strategy:
Strategy Games focus on thinking and planning to get victory, they are normally put into four sub-types, whether the game is real-time or turn-based and if it focuses on strategy or tactics. Most strategy video games have the player indirectly control game units under their command in a godlike view of the map.
Racing:
Racing games are either in a third-person perspective or first-person perspective, with the player normally taking part in a racing competition using any type sea, air or land vehicles. They can be anywhere between hardcore simulations and arcade racing games. There some sub-genres of racing games: Arcade-style racers (Burnout), Racing Simulators (Project Cars) and Kart racing games (Mario Kart).