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We propose a novel framework to learn how to communicate with intent, i.e., to transmit messages over a wireless communication channel based on the end-goal of the communication. This stays in stark contrast to classical communication systems where the objective is to reproduce at the receiver side either exactly or approximately the message sent by the transmitter, regardless of the end-goal. Our procedure is general enough that can be adapted to any type of goal or task, so long as the said task is a (almost-everywhere) differentiable function over which gradients can be propagated. We focus on supervised learning and reinforcement learning (RL) tasks, and propose algorithms to learn the communication system and the task jointly in an end-to-end manner. We then delve deeper into the transmission of images and propose two systems, one for the classification of images and a second one to play an Atari game based on RL. The performance is compared with a joint source and channel coding (JSCC) communication system designed to minimize the reconstruction error of messages at the receiver side, and results show overall great improvement. Further, for the RL task, we show that while a JSCC strategy is not better than a random action selection strategy even at high SNRs, with our approach we get close to the upper bound even for low SNRs.