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Inner
 Inner[f,  ,  , g] is a generalization of Dot in which f plays the role of multiplication and g of addition.
Example: Inner[f, a,b , x,y ,g]   .
Inner[f,  a,b , c,d  , x,y ,g]  .
Like Dot, Inner effectively contracts the last index of the first tensor with the first index of the second tensor. Applying Inner to a rank  tensor and a rank  tensor gives a rank  tensor.
Inner[f,  ,  ] uses Plus for g.
Inner[f,  ,  , g, n] contracts index n of the first tensor with the first index of the second tensor.
The heads of  and  must be the same, but need not necessarily be List.
See The Mathematica Book: Section 2.2.10 and Section 3.7.11.
See also: Outer, Thread, MapThread, ListCorrelate.
Further Examples
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