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The itinerary planning problem in an urban public transport system constitutes a common routing and scheduling decision faced by travelers. The objective of this paper is to present a new formulation and an algorithm for solving the itinerary planning problem, i.e., determination of the itinerary that lexicographically optimizes a set of criteria (i.e., total travel time, number of transfers, and total walking and waiting time) while departing from the origin and arriving at the destination within specified time windows. Based on the proposed formulation, the itinerary planning problem is expressed as a shortest path problem in a multimodal time-schedule network with time windows and time-dependent travel times. A dynamic programming-based algorithm has been developed for the solution of the emerging problem. The special case of the problem involving a mandatory visit at an intermediate stop within a given time window is formulated as two nested itinerary planning problems which are solved by the aforementioned algorithm. The proposed algorithm has been integrated in a Web-based journey planning system, whereas its performance has been assessed by solving real-life itinerary planning problems defined on the Athens urban public transport network, providing fast and accurate solutions.