As a well-known application of combinatorial optimization, influence maximization (IM) is formulated as selecting a set of initial users from a social network to maximize the expected number of influenced users. The integration of deep learning techniques into combinatorial optimization, specifically for solving the influence maximization problem, marks a significant advancement in understanding and leveraging complex social network dynamics. Traditional methods coupled with greedy/approximation/heuristic node selection algorithm with prescribed diffusion model (e.g., independent cascade (IC) and linear threshold (LT)) have provided foundational frameworks but fall short in capturing the stochastic and multifaceted nature of real-world information diffusion and node/graph characteristics. This handbook explores the limitations of these traditional models and introduces deep learning-based solutions, particularly graph neural networks (GNNs) and reinforcement learning (RL), which offer more flexible and adaptive approaches. By learning from data, these advanced methods can model intricate diffusion processes and optimize influence spread with greater precision and efficiency. This comprehensive overview encompasses foundational concepts, current methodologies, challenges, and future research directions, highlighting the transformative potential of deep learning in combinatorial optimization and influence maximization.