Networks (also known as graphs) are everywhere. People-contact networks, social networks, email communication networks, internet networks (among others) are examples of graphs in our daily life. The increasing size of these networks makes it harder to understand them. Instead, summarizing these graphs can reveal key patterns and also help in sensemaking as well as accelerating existing graph algorithms. Intuitively, different summarizes are desired for different purposes. For example, to stop viral infections, one may want to find an effective policy to immunize people in a people-contact network. In this case, a high-quality network summary should highlight roughly structurally important nodes. Others may want to detect communities in the same people-contact network, and hence, the summary should show cohesive groups of nodes. This implies that for each task, we should design a specific method to reveal related patterns. Despite the importance of task-specific summarization, there has not been much work in this area. Hence, in this thesis, we design task-specific summarization frameworks for univariate and multivariate networks. We start with optimization-based approaches to summarize graphs for a particular task and finally propose general frameworks which automatically learn how to summarize for a given task and generalize it to similar networks. 1. Optimization-based approaches: Given a large network and a task, we propose summarization algorithms to highlight specific characteristics of the graph (i.e., structure, attributes, labels, dynamics) with respect to the task. We develop effective and efficient algorithms for various tasks such as content-aware influence maximization and time segmentation. In addition, we study many real-world networks and their summary graphs such as people-contact, news-blogs, etc. and visualize them to make sense of their characteristics given the input task. 2. Learning-based approaches: As our next step, we propose a unified framework which learns the process of summarization itself for a given task. First, we design a generalizable algorithm to learn to summarize graphs for a set of graph optimization problems. Next, we go further and add sparse human feedback to the learning process for the given optimization task. To the best of our knowledge, we are the first to systematically bring the necessity of considering the given task to the forefront and emphasize the importance of learning-based approaches in network summarization. Our models and frameworks lead to meaningful discoveries. We also solve problems from various domains such as epidemiology, marketing, social media, cybersecurity, and interactive visualization. / Doctor of Philosophy / Networks (also known as graphs) are everywhere. People-contact networks, social networks, email communication networks, internet networks (among others) are examples of graphs in our daily life. The increasing size of these networks makes it harder to understand them. Instead, summarizing these graphs can reveal key information and also help in sensemaking as well as accelerating existing graph analysis methods. Intuitively, different summarizes are desired for different purposes. For example, to stop viral infections, one may want to find an effective policy to immunize people in a people-contact network. In this case, a high-quality network summary should highlight roughly important nodes. Others may want to detect friendship communities in the same people-contact network, and hence, the summary should show cohesive groups of nodes. This implies that for each task, we should design a specific method to reveal related patterns. Despite the importance of task-specific summarization, there has not been much work in this area. Hence, in this thesis, we design task-specific summarization frameworks for various type of networks with different approaches. To the best of our knowledge, we are the first to systematically bring the necessity of considering the given task to the forefront and emphasize the importance of learning-based approaches in network summarization. Our models and frameworks lead to meaningful discoveries. We also solve problems from various domains such as epidemiology, marketing, social media, cybersecurity, and interactive visualization.