I am MAthematics and MEchanical Engineering student and this is my senior year. For reserch and personal interest, I need to learn about contact mechanics. From where I should start and what is the prerequisites for this subject.
Start with either Slaughter's or Barber's book on linear elasticity where they deal with Hertzian non-adhesive contact and the theory that leads to that.
Once you know the basics, move on to K L Johnson's book on contact mechanics. That will give you a good feel for adhesive contact too along with various solution methods.
Beyond a point you will have to start finding numerical solutions. A good starting point is the book by Peter Wriggers (though I don't like the pedagogy in the book).
Once you know these three well, you can go to the scientific literature and start exploring the details of other solutions and approaches.