This thesis introduces a new representation for genetic sequences in the form of geometric points or vectors. It is based on the relative frequencies of the various (small) fixed length substrings of $k-tuples$ of the DNA or protein sequences. This effectively transforms the sequence from a variable sized string to fixed size vector. We show that this transformation preserves, under certain circumstances, the $edit^distince$ between sequences, a widely used measure for comparing genetic sequences. This fact is used to develop a linear time heuristic for sequence comparison, an improvement over the quadratic time dynamic programming based algorithms currently in widespread use. The transformation from a variable sized sequence to a fixed size vector representation allows computational geometric techniques to be applied to the study of genetic sequences. In particular, we develop a method of comparing several sequences simulatneously without having to compare each pair of sequences separately. This results in a substantial reduction in the complexity of the problem of multiple sequence comparison and clustering. This can be applied as a filter to extract interesting sets of sequences from a large database for more thorough study as well as an indexing method, to locate the database sequences most likely to be related to a query sequence.