This document discusses methods for constructing phylogenetic trees including distance-based and character-based approaches. Distance-based methods include UPGMA, Neighbor-Joining (NJ), and Fitch-Margoliash (FM) which use genetic distances between sequences. Character-based methods include Maximum Parsimony (MP) which finds the tree requiring the fewest evolutionary changes, and Maximum Likelihood (ML) which calculates the probability of the observed sequence changes. NJ is the fastest method while ML is the slowest but uses all available sequence data. The appropriate method depends on factors like number of sequences and computational requirements.