# Short Steps in Noncommutative Geometry

## TL;DR

This paper introduces the fundamental concepts of noncommutative geometry, focusing on the algebraic structures and geometric ideas that underpin the field, aiming to provide a foundational understanding.

## Contribution

It offers an overview of noncommutative geometry, emphasizing the algebraic and geometric frameworks essential for further study in the field.

## Key findings

- Clarifies the concept of noncommutative algebras and their geometric interpretation
- Highlights the importance of additional structures like topology or norm
- Provides foundational insights for studying noncommutative spaces

## Abstract

Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces that are locally presented by noncommutative algebras of functions (possibly in some generalized sense). A noncommutative algebra is an associative algebra in which the multiplication is not commutative, that is, for which $xy$ does not always equal $yx$; or more generally an algebraic structure in which one of the principal binary operations is not commutative; one also allows additional structures, e.g. topology or norm, to be possibly carried by the noncommutative algebra of functions. These notes just to start understand what we need to study Noncommutative Geometry.