In this seminar I will review the current status of the measurement of the Unitarity Triangle angles alpha, beta and gamma in the BaBar experiment at SLAC B-Factory. Starting from the now well established
measurement of the sin2b parameter in neutral B decays to charmonium states, I will discuss the results using charmless B decays, the latter being sensitive to new physics through penguin diagrams. The second
part of the seminar will focus on the strategies and results to disentangle tree and penguin contributions to extract alpha. Finally, a comprehensive discussion on the way and results to gamma will be presented. I will also discuss briefly the statistical interpretations of the experimental results on alpha and gamma
in terms of the fundamental phases. In all cases, there will be especial emphasis in the more recent techniques and results by the experiment.