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The objective of this thesis was to construct radiation hybrid (RH) maps and estimate linkage disequilibrium (LD) using high density SNP markers on chromosomes 19 (BTA19) and 29 (BTA29) and use these as a tool to detect QTL in dairy and beef cattle. We have constructed RH maps of BTA19 and BTA29 consisting of 555 and 253 SNP markers respectively using a 12,000 rad whole genome RH panel. When aligned with the third draft of bovine genome sequence assembly, there was a significant internal rearrangement of the markers involving displacement, inversion and flips within the scaffolds with some scaffolds being misplaced in the genome assembly. Many of these mapped markers (370 and 186 SNP markers on BTA19 and 29 respectively) were further utilized to quantify the extent of LD using the square of the correlation coefficient (r2) and to study the pattern of selection signatures in beef (Angus) and dairy (Holstein) breeds of Bos taurus. Along the chromosomes, patterns of LD were variable in both breeds and a minimum of 30,000 informative and evenly spaced markers would be required for whole genome association studies in cattle. In addition, chromosomal regions showing evidence of selection for economically important traits in Angus and Holstein were identified. Furthermore, the dense SNP markers were used to perform chromosome-wide scan to detect QTL for different economically important traits in beef and dairy cattle. Two approaches, single marker LD regression and Bayesian Monte Carlo Markov Chain, were used to map QTL. QTL for 10 and 5 traits in dairy cattle and for 2 and 1 trait in beef cattle on BTA19 and 29 respectively were detected using both approaches of QTL mapping. The QTL detected in this study are a step towards the identification of positional candidate genes controlling these traits. In addition, we have detected several SNPs influencing economically important traits in both beef and dairy cattle. Some SNPs have been validated in an independent cattle population and has the potential of being utilized in the marker assisted selection of cattle. / Animal Science