In this dissertation we study some computations and applications of Heegaard Floer correction terms. In particular we explore the correction terms for the double covers of the three-sphere branched along the Whitehead doubles of knots. As a consequence we show that Whitehead double and iterated double of some classes of knots are independent in the smooth knot concordance group. We also compute the correction terms of non-trivial circle bundles over oriented surfaces and discuss how they can be applied to four-dimensional topology.
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