Self Assembly of colloidal particles has been investigated widely in the past few years due to its importance in the bottom-up fabrication of useful complex structures in nature. Self-assembly is found to be enhanced by bringing in a certain amount of directionality to the pair interactions. One way of acquiring this directionality is to modify the surface of the colloidal particles in such a way that only part of it takes part in the pair interactions. These surface modifications or "patches" allow otherwise neutral or repulsive particles to self-assemble via attractive patches. Such particles, known as "patchy particles" are patterned with at least one well-defined patch through which the particle can experience a strongly anisotropic, highly directional interaction with other particles or surfaces. Oppositely charged bipolar colloids or colloids decorated with complementary DNA on their surfaces are special kinds of patchy particles where only patch and non-patch parts are attractive. These are classified as inverse patchy colloids (IPC). In this work, equilibrium self-assembly of IPC in two dimensions is reported using Monte Carlo simulations. Square and triangular crystals are found to be stable at 0.5 patch coverage. Upon decreasing the patch coverage to 0.33, the regular square crystal is destabilized; instead rhombic and triangular crystals are found to be stable. At low patch coverages such as 0.22 and 0.12, only triangular crystal is stabilized at high density. Particles of all the patch coverages show kinetically stable cluster phases of different shapes and sizes at low densities, and the average cluster size depends on the patch coverage and particle density. State diagrams showing all the stable phases for each patch coverage are presented. Ordered phases are characterized by bond order parameters and radial distribution function. The effect of polydispersity in patch coverage on the polarization of the stable structures is also studied. The study demonstrates that inverse patchy colloids can stabilize various ordered two-dimensional structures by tuning the size of the patch, density, and interaction strengths. We also model the pair potential of single patch IPCs analytically using Debye-Huckel approximation and compare the applicability of the model in simulations. The potential applications of patchy particles in the field of targeted drug delivery, fabrication of photonic crystals, molecular electronics, bio-mimicking colloids, self-propelling particles, and controlled loading of catalyst attract significant research opportunities in this field.