In this thesis, we work towards bridging the gap between two distinct areas: noisy text handling and text summarisation. The overall goal of the paper is to examine the effects of noise in the training of convolutional neural networks for text summarisation, with a view to understanding how to effectively create a noise-robust text-summarisation system. We look specifically at the problem of abstractive text summarisation of noisy data in the context of summarising error-containing documents from automatic speech recognition (ASR) output. We experiment with adding varying levels of noise (errors) to the 4 million-article Gigaword corpus and training an encoder-decoder CNN on it with the aim of producing a noise-robust text summarisation system. A total of six text summarisation models are trained, each with a different level of noise. We discover that the models with a high level of noise are indeed able to aptly summarise noisy data into clean summaries, despite a tendency for all models to overfit to the level of noise on which they were trained. Directions are given for future steps in order to create an even more noise-robust and flexible text summarisation system.