According to superstring theory there are 10 or 11 dimensions. The reason for two different numbers is extremely too complicated for just one post so I recommend you read Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the 10th Dimension by Michio Kaku. That book covers how pointlike particles are treated as vibrating strings and the ways they vibrate allowing for dimensions.
Here is a short YouTube video about 10 dimensions:
Here is a short YouTube video by the author (Michio Kaku) about 11 dimensions: