Disclosed are compositions and a method for amplification of nucleic acid sequences of interest. The disclosed method generally involves replication of a complex nucleic acid sample such as genomic samples using one, a few, or more primers such that, during replication, the replicated strands are displaced from the nucleic acid molecules in the sample by strand displacement replication of another replicated strand. It was discovered that highly complex nucleic acid samples can be efficiently amplified using only one or a few primers having specific nucleic acid sequences. The one or few primers are complementary to nucleic acid sequences distributed throughout nucleic acid in the sample.