Texts for Systematic Biology
An annotated (and probably very biased) list
Schuh, R.T. 2000. Biological Systematics: Principles and Applications. Cornell University Press, 236 + ix pp. This is a readable introduction to the basics, including zoological nomenclature. The discussion of methods is oriented mostly to parsimony methods.
Page, R.D.M. and E.C. Holmes. (1998). Molecular Evolution, A phylogenetic approach. Blackwell Science, 346 +v pp. A readable introduction to the basics of molecular evolution, now probably somewhat dated, and how these are addressed with phylogenetic methods.
Kitching, I.J. et al. (1998). Cladistics, The Theory and Practice of Parsimony Analysis, 2nd Edition. This is an excellent introduction to the basic principles of parsimony analysis, including things like successive approximations character weighting.
Felsenstein, J. (2004). Inferring Phylogenies. Sinauer Associates Inc, 664 + xx pp. Felsenstein tried to cover the entire gamut of phylogenetic methods, such as they were in 2004, with attention to the logical basis and computational complexities. Not the easiest reading, perhaps, but it's mostly all there, including approaches to sequence alignment.
Lemey, P., M. Salemi and A-M Vandamme, eds. (2009). The Phylogenetic Handbook, 2nd Edition. A somewhat more recent attempt to cover the entire field, with chapters by leading experts in the field. More comprehensive than Felsenstein (2004). Be sure to read the second edition, which was much improved over the first.