Although most people work with vector-based data, raster-based data allows for different types of analysis which can be very cool; for example, site suitability analysis which might use DEMs and slope models are nicely suited for real-world visualization and modeling.
Reviewing....raster is a simple data structure made up of cells on a grid. Each cell has one value (ex- one elevation value per cell; if the resolution is 20' then the cell doesn't represent anything more detailed than those 20'). Raster uses much larger file sizes but it is a simpler file structure. The smaller the cell size, the higher the resolution which equals a bigger file!!!
Okay, on to the new stuff again: map algebra is a cell by cell combination of raster data layers. You can perform different functions on the data such as + - * / but that depends on which software you have. Problems can pop up relating to different cell sizes and overlapping, but you can 'resample' to achieve like size cells.
Other types analysis are local (using only 1 cell), neighborhood (cell with surrounding) and global (using the whole raster layer) to look at different raster layers. Local functions use the raster calculator for spatial analysis, and we can also reclassify (this is not worded correctly, i think) Reclassification simplifies data and it reminds me of 'dissolve'.