In this thesis, we introduce a method for exploring a latent space of 3D shapes learned by a deep neural network. The main idea of our method is to enable the exploration of the latent space through the navigation of a 2D embedding. The method is based on a combination of Isomap dimensionality reduction and an inverse mapping function. Specifically, given a dataset of 3D shapes, we first train an autoencoder neural network to learn a latent representation for the dataset. Then, we reduce the dimensionality of the latent space to two dimensions with the Isomap method. The 2D embedding of the latent space allows a user to easily navigate through the embedding and sample new points. Our method then translates the sampled points back into latent vectors with an inverse mapping function, while the latent vectors are decoded by the neural network into 3D shapes that can be inspected by the user. The inverse mapping is made possible by posing it as a radial basis function (RBF) scattered interpolation problem. We demonstrate with qualitative experiments that our exploration method has advantages compared to alternative approaches such as interpolation and principal component analysis. We also show with quantitative experiments that our method enables a meaningful exploration of the latent space.iii Kaick, my research supervisor, for giving me the opportunity and immense support to make this research a reality. His encouragement, guidance and patience truly helped me to shape this research into what it is today. I would also like to thank Dr. David Mould, Dr. WonSook Lee for their thorough review of my work. Their valuable suggestions and useful critiques towards the thesis improved the quality of the work. I would like to thank GIGL lab and all the members for their encouragement and suggestions to prepare myself for the defense. I am also grateful to the School of Computer Science, Carleton University for accepting me as a research student and facilitating me with financial assistance to complete my degree. At last, I would like to thank my parents, sister, family members and my beloved husband for their unconditional love and support that encouraged me to complete my research.