small deformations on the surface of the manifold. It has recently been discovered that in condensed matter physics, it is possible to realize certain phases of matter that display unique physical properties that can be described by the existence of quantities analogus to the topological invariant $g$. One class of such materials is topological insulators. In this article we shall discuss this connection between the ideas of topology and topological invariants with condensed matter physics in the light of a beautiful toy model called the SSH model [@ssh1; @ssh2]. However, before introducing the SSH model, we give a brief review of the background physics and discuss band insulators in section \[sec:bandinsulators\]. In section \[sec:tightbinding\], we understand how metals and insulators are modelled using quantum mechanics by writing a [*tight-binding Hamiltonian*]{}. Then, in section \[sec:peierls\], we digress a little to explore Peierls instability, a special case of [*charge density waves*]{}. We then introduce the concept of Berry phase in section \[secbphase\] which forms the basis of the theory of topological Insulators. Finally, in section \[sec:sshmodel\], we introduce the SSH model and do a detailed analysis before giving concluding remarks in section \[sec:conclusions\].

The band insulators {#sec:bandinsulators}
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To understand the ideas 