.. _section 1.1:

1.1. Basic Constructions
===========================

This first section begins with the basic definitions and constructions, and then
proceeds quickly to an important calculation, the fundamental group of the circle,
using notions developed more fully in :ref:`§1.3 <section 1.3>`. More systematic methods of calculation
are given in :ref:`§1.2 <section 1.2>`. These are sufficient to show for example that every group is realized 
as the fundamental group of some space. This idea is exploited in the Additional
Topics at the end of the chapter, which give some illustrations of how algebraic facts
about groups can be derived topologically, such as the fact that every subgroup of a 
free group is free.

.. toctree::
    paths-and-homotopy
    the-fundamental-group-of-the-circle
    induced-homomorphisms
    exercises