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• There are 348 trilinear alternating forms in dimension 9 over GF(2). • There is a trilinear alternating form with trivial group of automorphisms. • There is only one trilinear alternating form with a transitive group of automorphisms. Let V be a finite-dimensional vector space over a finite field and let f be a trilinear alternating form over V. For such forms, we introduce two new invariants. Together with a generalized radical polynomial used for classification of forms in dimension 8 over GF(2), they are sufficient to distinguish between all trilinear alternating forms in dimension 9 over GF(2). To prove the completeness of the list of forms, we computed their groups of automorphisms. There are 31 degenerate and 317 nondegenerate forms. We point out some forms with either small or large automorphism group. [ABSTRACT FROM AUTHOR]