The field of Computer Vision has seen great accomplishments in the last decade due to the advancements in Deep Learning. With the advent of Convolutional Neural Networks, the task of image classification has achieved unimaginable success when perceived through the traditional Computer Vision lens. With that being said, the state-of-the-art results in the image classification task were produced under a closed set assumption i.e. the input samples and the target datasets have knowledge of class labels in the testing phase. When any real-world scenario is considered, the model encounters unknown instances in the data. The task of identifying these unknown instances is called Open-Set Classification. This dissertation talks about the detection of unknown classes and the classification of the known classes. The problem is approached by using a neural network architecture called Deep Hierarchical Reconstruction Nets (DHRNets). It is dealt with by leveraging the reconstruction part of the DHRNets to identify the known class labels from the data. Experiments were also conducted on Convolutional Neural Networks (CNN) on the basis of softmax probability, Autoencoders on the basis of reconstruction loss, and Mahalanobis distance on CNN's to approach this problem.