**1. Introduction**

Topology optimization (TO) is carried out to obtain an optimal structural layout [1]. It is one of the branches of optimization methods differing from size and shape optimization. As expected, as a type of optimization method, it has constant parameters, like applied loads, material type, etc., objective function and constraints which change for every problem, and lastly variable which are the parameters of the material layout. In shape optimization, it aimed to find the position of the member of the structure, while in size optimization, only finding the size of the members is enough. In both cases, there will be no change in the number of members. On the other hand, in topology optimization some part or member of the structure will be deleted and a new layout will be prepared [2]. It is generally preferred to use finite element method (FEM) as meshing eases to find the places to be deleted. But as an optimization algorithm, several kinds are used including both gradient-based such as optimality criteria methods and non-gradient-based algorithms such as genetic algorithm [3].

The topology optimization of structures has proven to be a valuable tool for the identification of the best concepts in early phases of the design process. It is widely used in lightweight design of structures in automotive and aerospace industry, as well as in civil engineering, material science, and biomechanics [1, 4, 5].

This chapter will give brief introduction on topology optimization and later give related studies under several classifications. There are several well-prepared and

intensely examined review studies in literature, but some of them are on specific application area (vibration problems [6], continuum structures [7]) or are on a specific methodology (evolutionary algorithms [8, 9], level-set methods [10]), or recent studies are not included [11, 12]. This study mostly aims to present recent studies while giving brief description on previous ones.
