This paper presents a tutorial on the properties of the memristor, a fourth ideal circuit element that relates charge and magnetic flux. The memristor complements the resistor, capacitor, and inductor as fundamental components of ideal electrical circuits. The existence of the memristor was predicted in 1971 based on symmetry arguments, but was experimentally demonstrated only recently. The paper discusses the properties of a single memristor, memristors in series and parallel, as well as ideal memristor-capacitor (MC), memristor-inductor (ML), and memristor-capacitor-inductor (MCL) circuits. It shows that the memristor has hysteretic current-voltage characteristics and that the ideal MC and ML circuits exhibit non-exponential charge and current decay with two time-scales. The paper also demonstrates that the ideal MCL circuit can be tuned from overdamped to underdamped by switching the polarity of the capacitor. The properties of the memristor are closely related to its internal dynamics, and the paper presents simple models that illustrate these effects. The tutorial complements the pedagogy of ideal circuit elements and their properties. The paper also discusses the behavior of ideal MC and ML circuits with arbitrary voltages and shows that the memristive effects are significant only in the transient region. The paper concludes by discussing the implications of the memristor's properties for real-world circuits and the challenges in creating and experimentally investigating basic electrical circuits.This paper presents a tutorial on the properties of the memristor, a fourth ideal circuit element that relates charge and magnetic flux. The memristor complements the resistor, capacitor, and inductor as fundamental components of ideal electrical circuits. The existence of the memristor was predicted in 1971 based on symmetry arguments, but was experimentally demonstrated only recently. The paper discusses the properties of a single memristor, memristors in series and parallel, as well as ideal memristor-capacitor (MC), memristor-inductor (ML), and memristor-capacitor-inductor (MCL) circuits. It shows that the memristor has hysteretic current-voltage characteristics and that the ideal MC and ML circuits exhibit non-exponential charge and current decay with two time-scales. The paper also demonstrates that the ideal MCL circuit can be tuned from overdamped to underdamped by switching the polarity of the capacitor. The properties of the memristor are closely related to its internal dynamics, and the paper presents simple models that illustrate these effects. The tutorial complements the pedagogy of ideal circuit elements and their properties. The paper also discusses the behavior of ideal MC and ML circuits with arbitrary voltages and shows that the memristive effects are significant only in the transient region. The paper concludes by discussing the implications of the memristor's properties for real-world circuits and the challenges in creating and experimentally investigating basic electrical circuits.