Deep learning techniques have achieved profound success in many challenging real-world applications, including image recognition, speech recognition, and machine translation. This success has increased the demand for developing deep neural networks and more effective learning approaches. The aim of this thesis is to consider the problem of learning a neural network classifier and to propose a novel approach to solve this problem under the Information Bottleneck (IB) principle. Based on the IB principle, we associate with the classification problem a representation learning problem, which we call ``IB learning". A careful investigation shows there is an unconventional quantization problem that is closely related to IB learning. We formulate this problem and call it ``IB quantization". We show that IB learning is, in fact, equivalent to the IB quantization problem. The classical results in rate-distortion theory then suggest that IB learning can benefit from a vector quantization approach, namely, simultaneously learning the representations of multiple input objects. Such an approach assisted with some variational techniques, result in a novel learning framework that we call ``Aggregated Learning (AgrLearn)", for classification with neural network models. In this framework, several objects are jointly classified by a single neural network. In other words, AgrLearn can simultaneously optimize against multiple data samples which is different from standard neural networks. In this learning framework, two classes are introduced, ``deterministic AgrLearn (dAgrLearn)" and ``probabilistic AgrLearn (pAgrLearn)". We verify the effectiveness of this framework through extensive experiments on standard image recognition tasks. We show the performance of this framework over a real world natural language processing (NLP) task, sentiment analysis. We also compare the effectiveness of this framework with other available frameworks for the IB learning problem.