The basic conception behind the given problem definition is to discuss the working, operations and complexity analyses of some advanced data structures. The Data structures that we have discussed further are Red-Black trees and Splay trees.Red-Black trees are self-balancing trees having the properties of conventional tree data structures along with an added property of color of the node which can be either red or black. This inclusion of the property of color as a single bit property ensured maintenance of balance in the tree during operations such as insertion or deletion of nodes in Red-Black trees. Splay trees, on the other hand, reduce the complexity of operations such as insertion and deletion in trees by splayingor making the node as the root node thereby reducing the time complexity of insertion and deletions of a node. Furthermore, amortized analysis, which emerged from aggregate analysis, is an optimistic approach that can be used to calculate the amount of time and space required for the execution of various operations. Amortized analysis considers the number of operations required during the execution of an algorithm rather than the number of inputs required thus overlooking the worst case run time per operation, which can be too pessimistic.