Probably the most fun out of the 1st year math courses (can't speak for 1C03). It's also very important for upper-year math - vector calculus, geometry, topology, group/ring/field/Galois theory..all that and more depends on a solid background in linear algebra.

You won't really be looking at mathematical 'structure' very much (in this context, just vector spaces), but you'll cover a good deal of material on systems of linear equations & matrices, linear combinations, span, basis & dimension, particular linear transformations, and properties of complex numbers. You'll also cover some particularly important properties of matrices (really, properties of transformations), like rank, nullity, and eigenvectors. In 2R03 (and 2X03), you'll get a better idea of the significance of vector spaces (if you want, PM me - or better yet, ask Mowicz - if you're curious about what I mean by 'structure').

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