Since various types of unmanned aerial vehicles (UAVs) with different hardware capabilities are introduced, we establish a foundation for the multi-layer aerial network (MAN). First, the MAN is modeled as K layer ANs, and each layer has UAVs with different densities, floating altitudes, and transmission power. To make the framework applicable for various scenarios in MAN, we consider the transmitter- and the receiver-oriented node association rules as well as the air-to-ground and air-to-air channel models, which form line of sight links with a location-dependent probability. We then newly analyze the association probability, the main link distance distribution, successful transmission probability (STP), and area spectral efficiency (ASE) of MAN. The upper bounds of the optimal densities that maximize STP and ASE are also provided. Finally, in the numerical results, we show the optimal UAV densities of an AN that maximize the ASE and the STP decrease with the altitude of the network. We also show that when the total UAV density is fixed for two layer AN, the use of single layer in higher(lower) altitude only for all UAVs can achieve better performance for low(high) total density case, otherwise, distributing UAVs in two layers, i.e., MAN, achieves better performance.