Functional data analysis (FDA) deals with the analysis and theory of data that are in the form of functions, images, or other objects. FDA encompasses statistical methods for analyzing such data, which are often infinite-dimensional. This paper provides an overview of FDA, starting with basic statistical concepts like mean and covariance functions, then covering core techniques such as functional principal component analysis (FPCA). FPCA is a key dimension reduction tool, useful for imputing sparsely observed functional data. Other dimension reduction methods are also discussed. The paper also reviews functional linear regression, clustering, and classification of functional data. Beyond linear methods, it touches on nonlinear approaches like additive models and time-warping. The paper concludes with a discussion of future directions. FDA is applied to data recorded continuously or intermittently, such as CD4 count data. Functional data can be dense or sparse, with sparse data being more challenging to analyze. The paper discusses estimation of mean and covariance functions, hypothesis testing, and simultaneous confidence bands for functional data. FPCA is a key technique for dimension reduction, converting infinite-dimensional data into finite-dimensional vectors. It is used for regression, classification, and modeling functional data. The paper also addresses challenges in FDA, such as inverse problems and the need for regularization. It discusses various applications of FDA, including functional correlation and regression, and highlights the importance of robust methods for handling outliers. The paper concludes with a discussion of future research directions in FDA.Functional data analysis (FDA) deals with the analysis and theory of data that are in the form of functions, images, or other objects. FDA encompasses statistical methods for analyzing such data, which are often infinite-dimensional. This paper provides an overview of FDA, starting with basic statistical concepts like mean and covariance functions, then covering core techniques such as functional principal component analysis (FPCA). FPCA is a key dimension reduction tool, useful for imputing sparsely observed functional data. Other dimension reduction methods are also discussed. The paper also reviews functional linear regression, clustering, and classification of functional data. Beyond linear methods, it touches on nonlinear approaches like additive models and time-warping. The paper concludes with a discussion of future directions. FDA is applied to data recorded continuously or intermittently, such as CD4 count data. Functional data can be dense or sparse, with sparse data being more challenging to analyze. The paper discusses estimation of mean and covariance functions, hypothesis testing, and simultaneous confidence bands for functional data. FPCA is a key technique for dimension reduction, converting infinite-dimensional data into finite-dimensional vectors. It is used for regression, classification, and modeling functional data. The paper also addresses challenges in FDA, such as inverse problems and the need for regularization. It discusses various applications of FDA, including functional correlation and regression, and highlights the importance of robust methods for handling outliers. The paper concludes with a discussion of future research directions in FDA.