We describe the construction and performance of an inexpensive modular Raman spectrometer that has been assembled in the framework of a fourth-year undergraduate project (costs below $5000). The spectrometer is based on a 4 mW 532 nm green laser pointer and a compact monochromator equipped with glass fiber optical connections, linear detector array, and a USB computer connection and power supply. Because of its backscattering geometry, the spectrometer can be used for liquid and solid samples and offers a spatial resolution below 100 [mu]m. With a spectral resolution of ca. 20 cm[superscript -1], accuracy of 2 cm[superscript -1], and a cutoff wavenumber below 340 cm[superscript -1], the Raman spectrometer has useful specifications. The apparatus is compact and portable. In conjunction with a laptop computer, it can be operated on batteries and would thus be suitable for field measurements. All components of the spectrometer are easily visible and accessible, which makes it ideally suited for lecture and teaching lab demonstrations unlike conventional "black box' instruments. We use this spectrometer for various undergraduate and graduate experiments and research, for analytical applications (e.g., determining alcohol content of beverages or purity of aspirin), and fundamental research (e.g., hydrogen bonding in solid aspirin or liquid water and temperature-dependence of the OH-stretching Raman band of liquid water). (Contains 5 figures.)