A method of detecting genetic variation in a subject's genome comprising: a. Providing a plurality of fragmented polynucleotides from the subject, which comprise target polynucleotides; b. Ligating a first partially single-stranded adapter to the target polynucleotides of step (a), wherein the partially single-stranded adapter has a double-stranded region at one end (sequence U hybridized to complementary sequence U') and the single-stranded sequence Y that does not hybridize to the target polynucleotide under the hybridization and extension conditions used, and further wherein ligation adds sequence Y to both 5' ends of the target polynucleotides; c. Hybridizing a plurality of different oligonucleotide primers, each having a different target-specific sequence W at the 3' end of the oligonucleotide primer, and a common sequence Z and extending the primers to produce an extended oligonucleotide with sequence Y' (complement of Y) at the 3' end; d. Amplifying the extended oligonucleotides with a pair of amplification primers comprising: i. A first amplification primer comprising sequence X and sequence Y, with sequence Y at the 3' end for hybridization to sequence Y '; ii. A second amplification primer comprising sequences V and Z, with Z at the 3' end for hybridization to sequence Z' of an extended X-Y primer; Wherein amplification produces a plurality of extended X-Y oligonucleotides comprising sequences X, Y, W', and Z' (5' to 3'; where W' is the complement of W, and Z' is the complement of Z) from the first amplification primer, and a plurality of sequences comprising V, Z, Y', and X' (5' to 3'; where X' is the complement of X) from the second amplification primer; e. Sequencing a plurality of different target polynucleotides, each contained in a polynucleotide comprising one strand comprising sequences V, Z, W, Y', and X' (from 5' to 3'), and another strand comprising sequences X, Y, W', Z', and V' (from 5' to 3'), with target polynucleotide sequence located between Z/Y' and between Z'/Y; f. Determining if the subject has a genetic variation based on the sequencing of step (e). a. Providing a plurality of fragmented polynucleotides from the subject, which comprise target polynucleotides; b. Ligating a first partially single-stranded adapter to the target polynucleotides of step (a), wherein the partially single-stranded adapter has a double-stranded region at one end (sequence U hybridized to complementary sequence U') and the single-stranded sequence Y that does not hybridize to the target polynucleotide under the hybridization and extension conditions used, and further wherein ligation adds sequence Y to both 5' ends of the target polynucleotides; c. Hybridizing a plurality of different oligonucleotide primers, each having a different target-specific sequence W at the 3' end of the oligonucleotide primer, and a common sequence Z and extending the primers to produce an extended oligonucleotide with sequence Y' (complement of Y) at the 3' end; d. Amplifying the extended oligonucleotides with a pair of amplification primers comprising: i. A first amplification primer comprising sequence X and sequence Y, with sequence Y at the 3' end for hybridization to sequence Y '; ii. A second amplification primer comprising sequences V and Z, with Z at the 3' end for hybridization to sequence Z' of an extended X-Y primer; Wherein amplification produces a plurality of extended X-Y oligonucleotides comprising sequences X, Y, W', and Z' (5' to 3'; where W' is the complement of W, and Z' is the complement of Z) from the first amplification primer, and a plurality of sequences comprising V, Z, Y', and X' (5' to 3'; where X' is the complement of X) from the second amplification primer; i. A first amplification primer comprising sequence X and sequence Y, with sequence Y at the 3' end for hybridization to sequence Y '; ii. A second amplification primer comprising sequences V and Z, with Z at the 3' end for hybridization to sequence Z' of an extended X-Y primer; e. Sequencing a plurality of different target polynucleotides, each contained in a polynucleotide comprising one strand comprising sequences V, Z, W, Y', and X' (from 5' to 3'), and another strand comprising sequences X, Y, W', Z', and V' (from 5' to 3'), with target polynucleotide sequence located between Z/Y' and between Z'/Y; f. Determining if the subject has a genetic variation based on the sequencing of step (e).