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, wherein the common sequences at the 5' end of each individual template in the library are not identical and not fully complementary to the common sequences at the 3' end of said template, the method comprising: 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 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 primer oligonucleotide is a tailed primer comprising a non-hybridising tail sequence at the 5' end, amplifying the extension products formed in the initial primer extension reaction by carrying out a solution-phase polymerase chain reaction, and collecting the amplification products of the PCR reaction to 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. 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 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 primer oligonucleotide is a tailed primer comprising a non-hybridising tail sequence at the 5' end, amplifying the extension products formed in the initial primer extension reaction by carrying out a solution-phase polymerase chain reaction, and collecting the amplification products of the PCR reaction to 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. <EOS>