a.b.c or Dot[a, b, c] gives products of vectors, matrices and tensors.
a.b gives an explicit result when a and b are lists with appropriate dimensions. It contracts the last index in a with the first index in b.
Various applications of Dot:
Examples: a, b . c, d .
a, b, c, d . x, y .
The result of applying Dot to two tensors and is the tensor . Applying Dot to a rank tensor and a rank tensor gives a rank tensor.
When its arguments are not lists, Dot remains unevaluated. It has the attribute Flat.
See The Mathematica Book: Section 1.8.3 and Section 3.7.5.
See also: Inner, Cross, Outer, NonCommutativeMultiply.
Related package: Calculus`VectorAnalysis`.