Methods for the creation of one or more user-defined mutations that can be located anywhere in a target sequence, such as in a gene are disclosed. These methods can be used on a single-stranded or double-stranded template and, for a single-stranded template, generally include: (a) conducting a first amplification reaction in the presence of a thermostable DNA polymerase and a thermostable DNA ligase to synthesize a mutagenized strand of DNA comprising at least one mutagenic oligonucleotide relative to a complementary single-stranded template DNA comprising a target nucleic acid molecule in a circular DNA vector; (b) conducting a second amplification reaction in the presence of a thermostable DNA polymerase and a thermostable DNA ligase to synthesize a complementary mutant strand of DNA; and (c) degrading the template DNA and non-covalently closed circular nucleic acid molecules to obtain a mutation-containing double-stranded DNA product.