Google 翻译生成的粗略草稿，质量较低。术语依照术语表，但句子可能有误；之后会由仔细的译文取代。
致读者
1. The Elements of Mathematics series takes up mathematics at their beginning, and gives complete proofs. In principle, it requires no particular knowledge of mathematics on the reader’s part, but only a certain familiarity with mathematical reasoning and a certain capacity for abstract thought. Nevertheless, it is directed especially to those who have a good knowledge of at least the content of the first year or two of a university mathematics course.
2. The method of exposition we have chosen is axiomatic, and normally proceeds from the general to the particular. The demands of proof impose a rigorously fixed order on the subject matter. It follows that the utility of certain considerations will not be immediately apparent to the reader unless he already has a fairly extensive knowledge of mathematics.
3. The series is divided into Books, and each Book into chapters. The Books already published, either in whole or in part, in the French edition, are listed below. When an English translation is available, the corresponding English title is mentioned between parentheses. Throughout the volume a reference indicates the English edition, when available, and the French edition otherwise.
E (S) 指定的 Théorie des Ensembles (集合论) 阿尔盖布尔 (代数) — A (A) 通用拓扑（一般拓扑）— TG (GT) Fonctions d’une Variable Réelle（实数变量的函数）— FVR (FRV) Espaces Vectoriels Topologiques（拓扑向量空间） — EVT (TVS) 积分（Integration）——INT（INT） 阿尔盖布尔交换 (交换代数) — AC (CA) 差异与分析变量 — VAR 群和 Algèbres de Lie（李群和李代数） — LIE (LIE) 理论光谱 — TS
在前六本书中（根据上述阶），文本中的每个叙述都假设仅已知那些在同一章中或在之前的章中已经讨论过的结果，顺序如下：S; A、章I至III； GT，章I至III； A、从章IV起； GT，从章IV开始； FRV； TVS； INT。
从第七本书开始，读者通常会找到它与其他书籍的逻辑关系的精确指示（前六本书始终被假定为已知）。
4. However we have sometimes inserted examples in the text that refer to facts the reader may already know but which have not yet been discussed in the series. Such examples are placed between two asterisks: .... Most readers will undoubtedly find that these examples help them to understand the text. In other cases, the passages between ... refer to results that are discussed elsewhere in the series. We hope that the reader will be able to verify the absence of any vicious circle.
5. The logical framework of each chapter consists of the definitions, the axioms, and the theorems of the chapter. These are the parts that have mainly to be borne in mind for subsequent use. Less important results and those which can easily be deduced from the theorems are labelled as "propositions", "lemmas", "corollaries", "remarks", etc. Those which may be omitted on a first reading are printed in small type. A commentary on a particularly important theorem occasionally appears under the name of "scholium".
为了避免繁琐的重复，有时方便地引入记号或仅在特定章或章的特定截面内有效的缩写（对于例，在仅与交换环，字有关的章） “环”始终表示“交换环”）。这些约定总是被明确提及，通常是在它们出现的章的开头。
6. Some passages in the text are designed to forewarn the reader against serious errors. These passages are signposted in the margin with the sign ("dangerous bend").
7. The Exercises are designed both to enable the reader to satisfy himself that he has digested the text and to bring to his attention results that have no place in the text but are nevertheless of interest. The most difficult exercises bear the sign ¶.
8. In general, we have adhered to the commonly accepted terminology, except where there appeared to be good reasons for deviating from it.
9. We have made a particular effort always to use rigorously correct language, without sacrificing simplicity. As far as possible we have drawn attention in the text to abuses of language, without which any mathematical text runs the risk of pedantry, not to say unreadability.
10. Since in principle the text consists of the dogmatic exposition of a theory, it contains in general no references to the literature. Bibliographical references are gathered together in Historical Notes. The bibliography which follows each historical note contains in general only those books and original memoirs that have been of the greatest importance in the evolution of the theory under discussion. It makes no pretense of any sort to completeness.
至于习题，我们认为总体上不值得指出它们的起源，因为它们来自许多不同的来源（原始论文、教科书、习题的集合）。
11. 对这个级数的部分的引用如下： a) 如果引用同一截面 (\S) 中出现的定理、公理或定义，则由其数引用。 b) 如果它们出现在同一个章的另一个截面中，则该截面也在参考文献中被引用。 c) 如果它们出现在同一本书的另一个章中，则引用章和截面。 d) 如果它们出现在另一个书中，则首先引用该书，并使用其标题的缩写。
结果摘要用字母 R 引用；因此S、R表示“集合论结果汇总”。