We introduce and analyse a general notion of fundamental group for noncommutative spaces, described by differential graded algebras. For this we consider connections on finitely generated projective bimodules over differential graded algebras and show that the category of flat connections on such modules forms a Tannakian category. As such this category can be realised as the category of representations of an affine group scheme G, which in the classical case is (the pro-algebraic completion of) the usual fundamental group. This motivates us to define G to be the fundamental group of the noncommutative space under consideration. The needed assumptions on the differential graded algebra are rather mild and completely natural in the context of noncommutative differential geometry. We establish the appropriate functorial properties, homotopy and Morita invariance of this fundamental group. As an example we find that the fundamental group of the noncommutative torus can be described as the algebraic hull of the topological group \((\mathbb Z+\theta \mathbb Z)^{2}\).

我们介绍和分析非可交换空间的基本群的一般概念，用微分渐变代数描述。为此，我们考虑了微分渐变代数上有限生成的射影双模上的连接，并证明了此类模块上平面连接的类别形成了坦纳克类别。这样，可以将该类别实现为仿射组方案G的表示形式的类别，在经典情况下，仿射组方案G是常规基本群（的代数完成）。这激励我们定义G成为正在考虑的非交换空间的基本组。在非交换微分几何的情况下，微分渐变代数所需的假设是相当温和的，并且是完全自然的。我们建立了这个基本族群的适当的函子性质，同态性和森田不变性。例如，我们发现非交换环的基本群可以描述为拓扑群\（（\ mathbb Z + \ theta \ mathbb Z）^ {2} \）的代数外壳。