We have developed an ultra-stable low temperature scanning tunneling microscope (LTSTM) for application in atomic scale spectroscopy and atom manipulation experiments. The design is based on the Besocke type microscope allowing the installation of the LTSTM within a liquid helium bath (LHe) cryostat in ultra-high-vacuum (UHV). The exclusive use of nonmagnetic materials allows STM-operation in magnetic fields up to 5 T without influencing the measurements. Compared to the frequently used "beetle" type STM the new design is characterized by increased eigenfrequencies and an improved mechanical stability. In conjunction with a triple-stage vibration isolation system the LTSTM is suited for high resolution measurements. Atomic resolution on close-packed metal surfaces is routinely achieved. Inherent thermal shielding of the complete tunneling assembly minimizes thermal drift to less than 2 Å/h. The microscope is calibrated by means of atomic resolution images of the "missing-row" reconstructed Au(110) surface at temperatures of 300 K, 77 K and 5 K. Sample preparation takes place on a variable temperature manipulator in situ in UHV. The system is equipped with standard surface preparation and analysis tools. Sample transfer to the STM is performed in UHV by a sample transfer system that includes as well a fast-load-lock for sample exchange without breaking the main vacuum. The microscope has been used to study the electronic surface state of Ag(111) at 5 K by topographic (STM) and spectroscopic (STS) measurements. The scattering of the surface state electrons off surface defects has been observed in topographic measurements. The spectroscopy data show the onset of the surface state at 65 meV below the Fermi energy. By locally resolved tunneling spectra the electron dispersion relation of the surface state has been determined. The data reveal that the surface state forms a nearly free, two-dimensional electron gas with an effective mass m* of the surface state electrons 0.41me. A pair of parallel surface steps acting as confining structures has been shown to cause a discrete spectrum of confined states. Finally, the structure of Ni adislands and their influence on the surface state are presented.