Exchange bias has been studied extensively for over half of a century but most of the researchhas been carried out in the configuration called parallel exchange bias. In this configuration,the cooling field and the measurement field are applied in the plane. Beside parallel exchange bias, there has been very little work carried out in the perpendicular configuration with the cooling field and the measurement field along the filmnormal. Perpendicular exchange bias is recently of renewed interest becauseit is relevant in the quest for a better understanding of the microscopic originof the exchange bias phenomenon and itmight lead to wide applications inmagnetic sensors, perpendicular recording media, perpendicular magnetic read heads and also magnetic randomaccess memories (MRAMs). In this thesis, the studies on perpendicular exchange bias in [MnPd/Co]10 multilayers are reported for the first time. Since the objective of the present thesis is to study the perpendicular exchange bias mechanism,the approach is to investigate both the parallel and perpendicular exchange biases. Besides, perpendicular anisotropy of the samples atlow and roomtemperatures is also investigated due to its important contribution to the effect. The present thesis consists of 4 chapters. Chapter 1is to give an overview on exchange bias in both theoretical and experimental research; and also previous studies on perpendicular exchange bias. Chapter 2focuses on the sample preparation and experimental techniques. Somedescriptions on the apparatuses and measurements thatwere used in the present thesis are introduced. Chapter 3represents the experimental results. The aim and configurations of measurements and also sample processing procedures are given. Chapter 4is to discuss the results ofcrystallographic and magnetic properties of [MnPd/Co]10multilayers. The behavior of exchange bias in both the parallel and perpendicular directions will be summarized. After that, based on that result and the magnetic anisotropy behavior of the samples, we try to give a phenomenological picture to explain the perpendicular exchange bias coupling mechanism. Finally, conclusions and further direction as well as the list of references are given at the end of the thesis.