The MuSe 2023 is a set of shared tasks addressing three different contemporary multimodal affect and sentiment analysis problems: In the Mimicked Emotions Sub-Challenge (MuSe-Mimic), participants predict three continuous emotion targets. This sub-challenge utilises the Hume-Vidmimic dataset comprising of user-generated videos. For the Cross-Cultural Humour Detection Sub-Challenge (MuSe-Humour), an extension of the Passau Spontaneous Football Coach Humour (Passau-SFCH) dataset is provided. Participants predict the presence of spontaneous humour in a cross-cultural setting. The Personalisation Sub-Challenge (MuSe-Personalisation) is based on the Ulm-Trier Social Stress Test (Ulm-TSST) dataset, featuring recordings of subjects in a stressed situation. Here, arousal and valence signals are to be predicted, whereas parts of the test labels are made available in order to facilitate personalisation. MuSe 2023 seeks to bring together a broad audience from different research communities such as audio-visual emotion recognition, natural language processing, signal processing, and health informatics. In this baseline paper, we introduce the datasets, sub-challenges, and provided feature sets. As a competitive baseline system, a Gated Recurrent Unit (GRU)-Recurrent Neural Network (RNN) is employed. On the respective sub-challenges' test datasets, it achieves a mean (across three continuous intensity targets) Pearson's Correlation Coefficient of .4727 for MuSe-Mimic, an Area Under the Curve (AUC) value of .8310 for MuSe-Humor and Concordance Correlation Coefficient (CCC) values of .7482 for arousal and .7827 for valence in the MuSe-Personalisation sub-challenge.