A transimpedance amplifier has been designed for scanning tunneling microscopy (STM). The amplifier features low noise (limited by the Johnson noise of the 1 GΩ feedback resistor at low input current and low frequencies), sufficient bandwidth for most STM applications (50 kHz at 35 pF input capacitance), a large dynamic range (0.1 pA to 50 nA without range switching) as well as a low input voltage offset. The amplifier is also suited for placing its first stage into the cryostat of a low-temperature STM, minimizing the input capacitance and reducing the Johnson noise of the feedback resistor. The amplifier may also find applications for specimen current imaging and electron-beam induced current measurements in scanning electron microscopy, and as a photodiode amplifier with a large dynamic range. This paper also discusses sources of noise including the often neglected effect of non-balanced input impedance of operational amplifiers, and describes how to accurately measure and adjust the frequency response of low-current transimpedance amplifiers.