Laparoscopy is an imaging technique that enables minimally-invasive procedures in various medical disciplines including abdominal surgery, gynaecology and urology. To date, publicly available laparoscopic image datasets are mostly limited to general classifications of data, semantic segmentations of surgical instruments and low-volume weak annotations of specific abdominal organs. The Dresden Surgical Anatomy Dataset provides semantic segmentations of eight abdominal organs (colon, liver, pancreas, small intestine, spleen, stomach, ureter, vesicular glands), the abdominal wall and two vessel structures (inferior mesenteric artery, intestinal veins) in laparoscopic view. In total, this dataset comprises 13195 laparoscopic images. For each anatomical structure, we provide over a thousand images with pixel-wise segmentations. Annotations comprise semantic segmentations of single organs and one multi-organ-segmentation dataset including segments for all eleven anatomical structures. Moreover, we provide weak annotations of organ presence for every single image. This dataset markedly expands the horizon for surgical data science applications of computer vision in laparoscopic surgery and could thereby contribute to a reduction of risks and faster translation of Artificial Intelligence into surgical practice.