Simple - a leaf with one leaf blade.
Compound - leaves that have their blades divided into several leaflets.
To distinguish whether a leaf is simple or compound, look for the lateral bud that typically forms at the axil of each leaf. if the axillary bud is not present the blade belongs to a leaflet, and therefore is part of a compound leaf.
On a compound leaf, leaflets may be arranged differently.
Palmately compound - leaflets arranged like the fingers on a hand.
Pinnately compound - leaflets are attached like the vanes of a feather. If the leaf consits of paired leaflets it is called even pinnately compound. If it has uneven number of leaflets, it is called uneven or odd pinnately compound.
Bipinnately compound - (or twice pinnately) leaflets of a pinnately compound leaf are divided themselves as well.
Thrice pinnately compound - leaflets are divided twice.
Trifoliolate - compound leaves with three leaflets.