This paper presents a general study of primordial scalar non-Gaussianities in single field inflationary models in Einstein gravity. The authors consider models where the inflaton Lagrangian is an arbitrary function of the scalar field and its first derivative, and the sound speed is arbitrary. They find that under reasonable assumptions, the non-Gaussianity is completely determined by five parameters. In special limits of the parameter space, one finds distinctive "shapes" of the non-Gaussianity. In models with a small sound speed, several of these shapes would become potentially observable in the near future. Different limits of our formulae recover various previously known results. The paper discusses several classes of inflationary models, including slow-roll inflation, DBI inflation, and K-inflation. For each model, the authors derive the cubic fluctuation Lagrangian in appropriate gauge-invariant variables and compute the non-Gaussianities. The main result is that there are only a few basic shapes, governed by 5 parameters in the most general model. The authors evaluate their results for the three special examples and present the different qualitative shapes of the non-Gaussianities that may occur. They also describe the effects of putting the inflaton in a vacuum other than the Bunch-Davies vacuum. The paper concludes with a discussion of the implications of these results for the inflationary vacuum and the potential for future experiments to detect non-Gaussianities. The authors also discuss the connection between non-Gaussianities and the structure of the three-point function, and the potential for using dS/CFT to study holographic descriptions of dS space.This paper presents a general study of primordial scalar non-Gaussianities in single field inflationary models in Einstein gravity. The authors consider models where the inflaton Lagrangian is an arbitrary function of the scalar field and its first derivative, and the sound speed is arbitrary. They find that under reasonable assumptions, the non-Gaussianity is completely determined by five parameters. In special limits of the parameter space, one finds distinctive "shapes" of the non-Gaussianity. In models with a small sound speed, several of these shapes would become potentially observable in the near future. Different limits of our formulae recover various previously known results. The paper discusses several classes of inflationary models, including slow-roll inflation, DBI inflation, and K-inflation. For each model, the authors derive the cubic fluctuation Lagrangian in appropriate gauge-invariant variables and compute the non-Gaussianities. The main result is that there are only a few basic shapes, governed by 5 parameters in the most general model. The authors evaluate their results for the three special examples and present the different qualitative shapes of the non-Gaussianities that may occur. They also describe the effects of putting the inflaton in a vacuum other than the Bunch-Davies vacuum. The paper concludes with a discussion of the implications of these results for the inflationary vacuum and the potential for future experiments to detect non-Gaussianities. The authors also discuss the connection between non-Gaussianities and the structure of the three-point function, and the potential for using dS/CFT to study holographic descriptions of dS space.