The A* algorithm finds the shortest path between two nodes on a graph. It is the most flexible algorithm that NavTiles provides. It supports pathfinding with area types with varying costs, dynamically changing grids, and does so for every available grid type (regular, isometric, and hexagonal). It is not as fast as the other pre-packaged algorithms, but it makes up for that with its flexibility.
For more information on A*, check out this Wikipedia page.