This book has grown out of an undergraduate course that I have taught at the Australian National University (ANU) for over 20 years. The course is one-semester long, which means that it runs for a total of 12 weeks. In each week I teach two lectures, where a lecture is defined as a 100-minute class with a 5-minute break in the middle. This lecture format is common in Europe but can be implemented almost everywhere; for example, at the ANU—where a normal teaching period is 50 minutes—I simply reserve two consecutive periods for every lecture. A 12-week semester can in principle accommodate 24 lectures of this kind but the course material only occupies 21, with the remaining time spent on discussing assignments, review, etc. While I was transforming my lecture notes into a book, I decided to keep the splitting of the course material into 21 lectures. This approach is unusual as most authors would organise the content into chapters, with each chapter accommodating a particular topic. However, I find that dividing the material according to the way it is presented at the lectures has several advantages compared to the traditional topicbased book composition. Indeed, first of all, the lecture-based organisation ensures that the content is partitioned into (approximately) equal pieces, so that none of them stands out and looks intimidating to the students at least as far as the length is concerned. This issue becomes particularly important for those who wish to use the book for self-study and would like to keep a close eye on their overall progress. Secondly, the lecture-based format guarantees that the students get more training for the more advanced topics, which are spread over several lectures. Indeed, each lecture has its own unique set of exercises, and the students are strongly encouraged to do at least some of them before moving on. It is then automatic that the harder the topic, the more exercises one is expected to do to go through it. It should also be mentioned that some of the exercises for each lecture serve as a preparation for the following one. Thirdly, the lecture-based split-up gives clear teaching guidelines to the instructor, at the same time allowing for the possibility of re-arranging the material according to their own taste. As the book covers a one-semester course, it is shorter than most complex analysis texts (approximately 200 pages). It is well-known that many students are intimi-

中文翻译：

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前言

本书源于我在澳大利亚国立大学 (ANU) 教授 20 多年的本科课程。该课程为期一个学期，这意味着它总共持续 12 周。我每周教两节课，其中一节课定义为 100 分钟的课程，中间有 5 分钟的休息时间。这种讲座形式在欧洲很常见，但几乎可以在任何地方实施；例如，在澳大利亚国立大学——那里的正常教学时间是 50 分钟——我只是为每堂课预留两个连续的时间段。一个12周的学期原则上可以容纳24节这样的课，但教材只占21节，剩下的时间花在讨论作业、复习等上。将课程材料分成 21 个讲座。这种方法很不寻常，因为大多数作者会将内容组织成章节，每章包含一个特定的主题。然而，我发现，与传统的基于主题的书籍组合相比，根据材料在讲座中的呈现方式来划分材料有几个优点。事实上，首先，以讲座为基础的组织确保内容被划分为（大约）相等的部分，这样至少就长度而言，它们中没有一个是突出的并且看起来对学生来说是令人生畏的。对于希望将本书用于自学并希望密切关注其整体进展的人来说，这个问题变得尤为重要。其次，以讲座为基础的形式保证学生得到更多关于更高级主题的培训，这些主题分布在几个讲座中。事实上，每堂课都有自己独特的一套练习，强烈鼓励学生在继续之前至少做一些练习。然后自然而然地，主题越难，人们期望通过它做的练习越多。还应该提到的是，每堂课的一些练习是为下一场做准备。第三，基于讲座的拆分为教师提供了清晰的教学指导，同时允许根据自己的口味重新安排材料的可能性。由于本书涵盖了一个学期的课程，因此它比大多数复杂的分析文本（大约 200 页）都要短。众所周知，很多学生都被吓到了 强烈鼓励学生在继续之前至少做一些。然后自然而然地，主题越难，人们期望通过它做的练习越多。还应该提到的是，每堂课的一些练习是为下一场做准备。第三，基于讲座的拆分为教师提供了清晰的教学指导，同时允许根据自己的口味重新安排材料的可能性。由于本书涵盖了一个学期的课程，因此它比大多数复杂的分析文本（大约 200 页）都要短。众所周知，很多学生都被吓到了 强烈鼓励学生在继续之前至少做一些。然后自然而然地，主题越难，人们期望通过它做的练习越多。还应该提到的是，每堂课的一些练习是为下一场做准备。第三，基于讲座的拆分为教师提供了清晰的教学指导，同时允许根据自己的口味重新安排材料的可能性。由于本书涵盖了一个学期的课程，因此它比大多数复杂的分析文本（大约 200 页）都要短。众所周知，很多学生都被吓到了 还应该提到的是，每堂课的一些练习是为下一场做准备。第三，基于讲座的拆分为教师提供了清晰的教学指导，同时允许根据自己的口味重新安排材料的可能性。由于本书涵盖了一个学期的课程，因此它比大多数复杂的分析文本（大约 200 页）都要短。众所周知，很多学生都被吓到了 还应该提到的是，每堂课的一些练习是为下一场做准备。第三，基于讲座的拆分为教师提供了清晰的教学指导，同时允许根据自己的口味重新安排材料的可能性。由于本书涵盖了一个学期的课程，因此它比大多数复杂的分析文本（大约 200 页）都要短。众所周知，很多学生都被吓到了