The Vector Mode in the Second-order Cosmological Perturbation TheoryThis thesis sheds valuable new light on the second order cosmological perturbation theory, extensively discussing it in the context of cosmic microwave background (CMB) fluctuations. It explores the observational consequences of the second order vector mode, and addresses magnetic field generation and the weak lensing signatures, which are key phenomena of the vector mode. The author demonstrates that the second order vector mode, which never appears