Mutations are changes in DNA that can be caused spontaneously due to errors during DNA replication or induced by mutagenic agents like radiation and chemicals. There are two main categories of mutations: somatic mutations, which occur in body cells and are not passed to offspring, and germline mutations, which occur in sex cells and can be inherited. Common types of mutations include substitutions, insertions, deletions, and frameshift mutations. Bacteria have multiple DNA repair mechanisms like excision repair, photoreactivation, and post-replication repair to fix mutations through processes like removing and replacing damaged sections of DNA.