随着当今收集数据能力的增强，函数型数据已经逐渐成为了一种常见的数据类型，在为统计学家提供更多信息的同时对传统的统计方法提出了挑战。本文主要基于J.O.Ramsay和B.W.Silverman所著的《Functional Data Analysis》一书，总结了函数型数据分析的重要方法，然后结合当下函数型数据的研究成果进行综述，最后加入了随机模拟试验和对真实数据的分析案例，为函数型数据分析的进一步研究学习奠定基础。首先本文通过学习书内 知识介绍了函数型数据有别于传统数据的个性特点，以及分析前需要的一些预处理和简单描述方法。然后，针对数据的函数性，在理解书中讲解的基础上给出了充分的解读，并且利用书中的光滑方法对函数性进行刻画和控制在实现了数据与函数的互通后，进一步学习了函数型数据的主成分分析和线性模型两个最常用的方法，从理论上介绍了方法的性质和基本形式，在计算上介绍如何实现近似和评估拟合程度。最后，进行了控制拟合光滑性的模拟试验，并应用主成分分析对加拿大气温数据进行了分析。

The capability to collect huge amount of data has make the functional data become accessible and common-used. Such new data type provide statisticians with more chance, meanwhile they require more powerful tools to analysis. This paper is mainly based on the book Functional Data Analysis written by J.O.Ramsay and B.W.Silverman, and summarizes fundamental functional data analysis methods. Combined with some new work in this track, the paper gives review of them.Eventually, some simulation and real data case are included. This paper paves the way to further functional data analysis study and research in future. In this paper,according to book, first to reveal what is ’functional’, and then introduce preparation and descriptive tools for analysis. Using smoothing method in book can reveal the functional character of data and control how smooth result is. After smoothing, the paper introduces functional principal component analysis as well as functional linear model, and includes some property of them theoretically. For computation, some trick for use these method in practice is also explained. Lastly, some simulation work indicates how to control smoothness of results and the functional principal component analysis of Canadian temperature data are contained.