This information is part of the Modelica Standard Library maintained by the Modelica Association.
Overview
Overview of Modelica Library
The Modelica Standard Library consists of the following main sublibraries:
Library Components  Description 

Analog Analog electric and electronic components, such as resistor, capacitor, transformers, diodes, transistors, transmission lines, switches, sources, sensors. 

Machines Electrical asynchronous, synchronous, and DCmachines (motors and generators) as well as 3phase transformers. 

FluxTubes Based on magnetic flux tubes concepts. Especially to model electromagnetic actuators. Nonlinear shape, force, leackage, and material models. Material data for steel, electric sheet, pure iron, Cobalt iron, Nickel iron, NdFeB, Sm2Co17, and more. 

Translational 1dim. mechanical, translational systems, e.g., sliding mass, mass with stops, spring, damper. 

Rotational 1dim. mechanical, rotational systems, e.g., inertias, gears, planetary gears, convenient definition of speed/torque dependent friction (clutches, brakes, bearings, ..) 


MultiBody 3dim. mechanical systems consisting of joints, bodies, force and sensor elements. Joints can be driven by drive trains defined by 1dim. mechanical system library (Rotational). Every component has a default animation. Components can be arbitrarily connected together. 
FluidHeatFlow, HeatTransfer Simple thermofluid pipe flow, especially to model cooling of machines with air or water (pipes, pumps, valves, ambient, sensors, sources) and lumped heat transfer with heat capacitors, thermal conductors, convection, body radiation, sources and sensors.  

Blocks Input/output blocks to model block diagrams and logical networks, e.g., integerator, PI, PID, transfer function, linear state space system, sampler, unit delay, discrete transfer function, and/or blocks, timer, hysteresis, nonlinear and routing blocks, sources, tables. 
StateGraph Hierarchical state machines with a similar modeling power as Statecharts. Modelica is used as synchronous action language, i.e. deterministic behavior is guaranteed 

A = [1,2,3; 3,4,5; 2,1,4]; b = {10,22,12}; x = Matrices.solve(A,b); Matrices.eigenValues(A); 
Math,
Utilities Functions operating on vectors and matrices, such as for solving linear systems, eigen and singular values etc., and functions operating on strings, streams, files, e.g., to copy and remove a file or sort a vector of strings. 