texture>. this is like UV map in max. Automatic mapping is the same as flatten in the uv editor. Although its less inteligent about angles and maintaining the size of faces.

Subdivide. is like insert vertex. It places one or more vertexes right in the middle of an edge. Works in edge mode.

Split Polygon Tool. this is the cut tool. works by clicking on an edge and draking the new vert to were you want it. to place a vert right on an existing vert simply click on the edge connected to it and slide it over top. If you try and just click on the existing vert you will get an extra. You can use backspace to go back on step.

Extrude Face. This tool works a bit diffent from max. What you get when you click on, it is an extrude gizmo in the 3d view. For the most part i dont touch the gismo unless i have to move or scale on the normal. Insted i simpy hit W or R for move or rotate, and translate it normaly. You should be carfull not to forget to move the new extrude.

Extrude Edge. Same as above. One thing though, maya will allow you to make non-maniflold geomatry. meening that you can take a continues mesh and extrude a edge from it. (this is bad news by the way)

Bevel. This is the same as chamfer edge. An in versions of maya 6.5 or greater works well.

Cut Faces Tool. This works like Quick slice.

Merge Vertices. Wield vertex

Collapse. works in edge mode and is the same as in max.

Fill Hole. This is sort of like cap in border mode in max. just select an edge (that has a hole attacted to it) and it will fill that hole.

Sculpt Polygons Tool. This is the same as painting relax or what ever in max.

Selection>. You can find some interesting selection tools in here. like every other edge or random face that sort of thing. (is a little bit hectic to set up though)

Normals>. Hard and soft edges, works in edge mode and is maya's "smoothing groups" you'll find other things in here like flip normals and lock unlock normals. if your shoping for normals this is the place.