High frequency financial data does provide enough material to the estimation of volatil-ity including integrated volatility and spot volatility, but high frequency sampling makes the nonnegligible effect of market microstructure noise on the estimation of volatility, How to remove the effect is a hot topic, which has been studied by many researchers in recent years. As another significant feature of high frequency data, mul-tiple records, also brings trouble to the estimation of volatility. The thesis makes its own contribution in the new field. In the first part of this thesis, we introduce the features of high frequency financial data, which are widely accepted by researchers. We make a review of some basic concepts and assumptions on modeling the data. After knowing the features of real financial data, we display the motivation and necessity of our research. The main research topic of this thesis is to study the estimation of volatility under presence of noise and multiple records, and discuss the effect of multiple records on spot volatility. In the second part, we employ the minimum and maximum methods to estimate in-tegrated volatility under the presence of multiple records. Then, based on the idea, we propose a measure of integrated volatility with possible presence of multiple records and one-sided noise, The estimator is valid under mild conditions and it is easy to be implemented. The finite sample performance of the proposed estimator has been verified by simulation studies. We apply it to real high frequency data as well. In the third part, we propose a range-based estimator of integrated volatility in the presence of multiple records. The asymptotic properties are established under mild conditions, The estimator outperforms the existing approaches. In simulation studies, several common models are employed to justify the performance of the estimator. The fourth part is devoted to spot volatility estimation in the presence of multiple records and two-sided noise. The estimator is constructed by range returns and kernel method. We prove the consistency and asymptotic normality of the new estimator, and several simulation studies support our theoretical results. In empirical analysis, the estimator is applied to real financial data, and an relationship between multiple records and spot volatility is discussed in real financial market. Finally, we make a conclusion of this thesis, and list some possible research topics in our further study.