Multi-agent systems (MASs) have emerged as a fundamental paradigm for coordinating, sharing knowledge, and collaboratively solving complex problems in distributed environments, especially with the rapid advancement of generative AI and autonomous agents. This tutorial provides a comprehensive introduction to the fundamentals of MASs, exploring state-of-the-art methodologies, architectural patterns, and key challenges in designing scalable distributed applications. In addition to the theoretical foundation, participants will engage with practical implementations using LangGraph, a widely adopted framework for building collaborative AI agent workflows.