The aim of this thesis is to get to know the process of making a 3D game for the Android platform using the Unity game engine. In the first part of this thesis we describe some basic concepts, which come in handy when making games, as we come across them when making almost all games. These are vectors and certain operations over them, 3D modeling, which is used to make the majority of objects, we see in a game, and ways of lighting these objects. Then we talk about physics engines, collision detection and introduce three popular physics engines. In the next part of the thesis we talk about different ways of making games and give some general information about game engines. After this part we represent the Android platform, here we talk about its architecture, give some useful information and talk a few words about game engines, which can be used to make games for this platform. The following chapter gives information about the Unity game engine, especially its characteristics and functions it provides. In the next chapter we again talk about the Unity game engine, this time about the process involved when making games using this game engine. The last chapter of the thesis is dedicated to our work in practice. In it we describe how we made our 3D game, which we tested on an Android smart phone.