Abstract
This paper extends the investigation of the invariants of the Riemann tensor to include the invariants that are of odd degree in the trace-free Ricci tensor. It is shown that these invariants can be expressed in terms of 15 such invariants that are irreducible. As a consequence, it is possible to write down a complete set of invariants of the Riemann tensor. Several syzygies for these invariants have been found and examples of these are given. These syzygies suggest there may be several new syzygies of invariants with even degree in the trace-free Ricci tensor. A large number of these have also been found and are discussed in the paper.
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