The field of recommendation algorithms has undergone a remarkable evolution. Early systems were built on simple statistical methods that leveraged direct user-item interactions. These foundational techniques, known as collaborative filtering, gave way to more sophisticated latent factor models, which sought to uncover the hidden dimensions of user preference by decomposing the user-item interaction matrix. The deep learning revolution subsequently ushered in a new era, with neural networks enabling the modeling of complex, non-linear relationships that were previously intractable.

This progression continued with the development of specialized architectures to capture the sequential dynamics of user behavior, borrowing heavily from advances in natural language processing. Concurrently, a new perspective emerged that modeled the recommendation problem as a graph, applying Graph Neural Networks to capture high-order relationships between users and items. Most recently, the landscape is being reshaped by the advent of large-scale generative models, including Generative Adversarial Networks, Diffusion Models, and, most notably, Large Language Models (LLMs), which are redefining the boundaries of what recommender systems can achieve.

This book aims to provide a structured, high-level, and practical overview of this algorithmic landscape. We organize our survey into several principal sections based on the primary data modality and methodological approach each class of algorithms leverages:

1. Foundational and Heuristic-Driven Algorithms. Models that rely on intrinsic item attributes (Content-Based) or manually defined heuristics (Rule-Based) to generate recommendations, offering interpretability and effectiveness for cold-start scenarios.
2. Interaction-Driven Recommendation Algorithms. The core of collaborative filtering, where models rely exclusively on user-item interaction data (e.g., ratings, clicks, purchases).
3. Context-Aware Recommendation Algorithms. Advanced models that leverage explicit side features and contextual information, crucial for industrial applications like CTR prediction.
4. Text-Driven Recommendation Algorithms. Models that incorporate unstructured text, such as user reviews or item descriptions, and are increasingly powered by LLMs.
5. Multimodal Recommendation Algorithms. Models that fuse information from multiple sources, such as text and images, to create a holistic understanding of items and preferences.
6. Knowledge-Aware Recommendation Algorithms. Advanced models that leverage structured knowledge from external sources like knowledge graphs.
7. Specialized Recommendation Tasks. A look at crucial sub-fields like ensuring fairness, mitigating bias, and addressing the cold-start problem.
8. New Algorithmic Paradigms. An exploration of emerging paradigms that extend beyond traditional recommendation, focusing on long-term value, causality, and transparency.
9. Evaluating Recommender Systems. A practical guide to the metrics and methodologies used to measure the performance and quality of recommender systems.

For each algorithm, we provide a concise explanation of its core concept, key differentiators, primary use cases, and practical considerations for implementation, along with a link to its seminal paper. Our objective is to equip engineers and researchers with a comprehensive map to navigate the field, understand its historical trajectory, and make informed decisions when designing and deploying the next generation of recommender systems.