Part 1 of a technical article by M. Luedtke of Berlin on the microscopic structure of vegetable fiber cells, drawing mainly on bamboo and bleached straw fibers. It covers transverse (annular) elements that cause bead-like swelling in cuprammonium solution, the layered structure of the cell wall, spiral lamellae, fibrils, and the binding material between them. The author argues that thin membranes similar to the cuticle separate the layers and lamellae and give the fiber strength. It includes micrographs, a labeled sketch of fiber structure and extensive footnotes citing botanical literature; it ends with "To be continued".