---
product_id: 317047593
title: "Springer An Introduction to Manifolds"
price: "£78.07"
currency: GBP
in_stock: true
reviews_count: 5
url: https://www.desertcart.co.uk/products/317047593-springer-an-introduction-to-manifolds
store_origin: GB
region: United Kingdom
---

# Comprehensive graduate-level text Builds deep conceptual mastery Includes exercises with hints & solutions Springer An Introduction to Manifolds

**Price:** £78.07
**Availability:** ✅ In Stock

## Summary

> 📘 Unlock the geometry of the universe — before your peers do!

## Quick Answers

- **What is this?** Springer An Introduction to Manifolds
- **How much does it cost?** £78.07 with free shipping
- **Is it available?** Yes, in stock and ready to ship
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## Key Features

- • **Concise Yet Complete:** Minimal prerequisites and well-structured content make advanced topics accessible without fluff.
- • **Trusted by the Academic Elite:** 4.8-star rating from 157 reviews confirms its status as a must-have for graduate students.
- • **Bridges Theory and Application:** Connects abstract math to physics fields like relativity and quantum theory for real-world relevance.
- • **Master Manifolds with Confidence:** Streamlined, clear exposition perfect for rapid mastery of complex geometry and topology.
- • **Self-Study Friendly with Guided Support:** Hints and solutions empower independent learners to validate and deepen understanding.

## Overview

Springer's 'An Introduction to Manifolds' is a highly regarded graduate-level textbook that offers a concise, well-structured introduction to manifolds, blending algebra, topology, and analysis. It features exercises with hints and solutions, making it ideal for both classroom use and self-study. With minimal prerequisites, it prepares readers to tackle advanced geometry and topology topics, while connecting theory to applications in physics. Praised for clarity and depth, it holds a 4.8-star rating from over 150 reviews.

## Description

Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.

Review: Concise introduction. Very readable. - Bought this book since my university completely didn't care to teach it's mathematicians any geometry beyond Euclidean... For me this book is quite concise I worked trough the entire book during the last two weeks. It consists of a lot of small subsegments that are easily understood. Not too much unnecessary text very well structured. Cannot say how understandable it is for non mathematicians, however it for for me self studying geometry. Will see how it works now as reference manual.
Review: Great Text and Clear Exposition - When I first began reading the text, I had a difficult time understanding the concepts, but the presentation of the material really laid bare all of the esoteric topics that I hadn't encountered formally before. Loring Tu has done an excellent job of making sure even the uninitiated student can make his/her way through this text, having sprinkled a few easy exercises through the text itself to emphasize the learning and familiarity with definitions, with more difficult exercises at the end (including computations as well as topics that force a student to understand and digest the section immediately preceding the problems). He labels every problem, so a student doesn't wade through pages of text needlessly trying to discover which part of the text will be most useful, but this method allows the student to hone in on the material which is exactly pertinent to that problem. I am by far not the best and brightest student, but I have been able to read the text and given a few hours for each section, complete all exercises throughout the reading and at the end of the section. With many hints and solutions at the end of the textbook, I can be sure I'm not only learning the material, I'm learning it correctly! I would agree with some of the other reviewers that this should be a text every graduate student in mathematics should read. It is not out of the realm of possibilities for a student to read it on his/her own, and the enlightenment gained from the generalizations of multivariate calculus is really a gift to oneself, as well as to any future students the person may have, for they will be able to answer any up-and-coming student's questions with a clarity surpassing any instructor I've personally had, which would have been very helpful as a budding mathematician.

## Features

- Item Category: Abis Book
- Item Trademark: SPRINGER
- Manufacturer: Springer-Verlag New York Inc.

## Technical Specifications

| Specification | Value |
|---------------|-------|
| Customer Reviews | 4.8 out of 5 stars 157 Reviews |

## Images

![Springer An Introduction to Manifolds - Image 1](https://m.media-amazon.com/images/I/51Wl1T+JpZL.jpg)

## Customer Reviews

### ⭐⭐⭐⭐⭐ Concise introduction. Very readable.
*by D***B on 20 September 2022*

Bought this book since my university completely didn't care to teach it's mathematicians any geometry beyond Euclidean... For me this book is quite concise I worked trough the entire book during the last two weeks. It consists of a lot of small subsegments that are easily understood. Not too much unnecessary text very well structured. Cannot say how understandable it is for non mathematicians, however it for for me self studying geometry. Will see how it works now as reference manual.

### ⭐⭐⭐⭐⭐ Great Text and Clear Exposition
*by A***Y on 3 February 2013*

When I first began reading the text, I had a difficult time understanding the concepts, but the presentation of the material really laid bare all of the esoteric topics that I hadn't encountered formally before. Loring Tu has done an excellent job of making sure even the uninitiated student can make his/her way through this text, having sprinkled a few easy exercises through the text itself to emphasize the learning and familiarity with definitions, with more difficult exercises at the end (including computations as well as topics that force a student to understand and digest the section immediately preceding the problems). He labels every problem, so a student doesn't wade through pages of text needlessly trying to discover which part of the text will be most useful, but this method allows the student to hone in on the material which is exactly pertinent to that problem. I am by far not the best and brightest student, but I have been able to read the text and given a few hours for each section, complete all exercises throughout the reading and at the end of the section. With many hints and solutions at the end of the textbook, I can be sure I'm not only learning the material, I'm learning it correctly! I would agree with some of the other reviewers that this should be a text every graduate student in mathematics should read. It is not out of the realm of possibilities for a student to read it on his/her own, and the enlightenment gained from the generalizations of multivariate calculus is really a gift to oneself, as well as to any future students the person may have, for they will be able to answer any up-and-coming student's questions with a clarity surpassing any instructor I've personally had, which would have been very helpful as a budding mathematician.

### ⭐⭐⭐⭐⭐ Parfait
*by A***T on 5 May 2019*

Très bon livre d’introduction ! Achat pas parfait !

## Frequently Bought Together

- An Introduction to Manifolds (Universitext)
- Differential Geometry: Connections, Curvature, and Characteristic Classes (Graduate Texts in Mathematics, 275)
- Introduction to Smooth Manifolds (Graduate Texts in Mathematics, Vol. 218)

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*Last updated: 2026-07-01*