Van Kampen's Theorem

Van Kampen's Theorem is a tool used in topology to determine the fundamental group of a complex space. It states that if a shape can be broken into two overlapping parts with known fundamental groups, then its overall fundamental group can be constructed from these parts. Essentially, it lets us understand the basic loops of a complicated space by analyzing simpler pieces and how they connect. This helps in studying the space's overall structure by piecing together local information, much like assembling a puzzle from its individual sections.