A method of generating a library of template polynucleotide molecules which have common sequences at their 5' ends and common sequences at their 3' ends, the method comprising: providing one or more blunt end target polynucleotide duplexes, adding a single 'A' deoxynucleotide to both 3' ends of the target polynucleotide duplexes, thereby producing a one-base 3' overhang, ligating identical mismatched adapter polynucleotides to both ends of each of one or more target polynucleotide duplexes to form one or more adapter-target constructs, wherein each mismatched adapter is formed from two annealed polynucleotide strands that form a bimolecular complex comprising at least one double-stranded region and an unmatched region, and wherein each mismatched adapter comprises a one-base 3' 'T' overhang on the double-stranded end, which is complementary to the one-base 3' 'A' overhang on the target polynucleotide duplexes, carrying out an initial primer extension reaction in which a primer oligonucleotide is annealed to an adapter portion of each of the adapter-target constructs and extended by sequential addition of nucleotides to form extension products complementary to at least one strand of each of the adapter-target constructs, wherein the extension products, and optionally amplification products derived therefrom, collectively provide a library of template polynucleotide molecules which have common sequences at their 5' ends and common sequences at their 3' ends; wherein the target polynucleotide duplexes to be ligated are a complex mixture of genomic DNA fragments representing a whole or substantially whole genome, and wherein the library of template polynucleotide molecules generated is representative of the whole or substantially whole genome. providing one or more blunt end target polynucleotide duplexes, adding a single 'A' deoxynucleotide to both 3' ends of the target polynucleotide duplexes, thereby producing a one-base 3' overhang, ligating identical mismatched adapter polynucleotides to both ends of each of one or more target polynucleotide duplexes to form one or more adapter-target constructs, wherein each mismatched adapter is formed from two annealed polynucleotide strands that form a bimolecular complex comprising at least one double-stranded region and an unmatched region, and wherein each mismatched adapter comprises a one-base 3' 'T' overhang on the double-stranded end, which is complementary to the one-base 3' 'A' overhang on the target polynucleotide duplexes, carrying out an initial primer extension reaction in which a primer oligonucleotide is annealed to an adapter portion of each of the adapter-target constructs and extended by sequential addition of nucleotides to form extension products complementary to at least one strand of each of the adapter-target constructs, wherein the extension products, and optionally amplification products derived therefrom, collectively provide a library of template polynucleotide molecules which have common sequences at their 5' ends and common sequences at their 3' ends; wherein the target polynucleotide duplexes to be ligated are a complex mixture of genomic DNA fragments representing a whole or substantially whole genome, and wherein the library of template polynucleotide molecules generated is representative of the whole or substantially whole genome.