Mock-Modular Forms of Weight One

In this thesis, we will study mock-modular forms of weight one and their Fourier coefficients. In particular, we will concentrate on the mock-modular forms whose shadows are dihedral newforms arising from ray class group characters of imaginary quadratic fields. We will show that certain linear combinations of their Fourier coefficients are logarithms of CM values of the modular j-function. We will also make a conjecture about the algebraicity of the individual Fourier coefficients.