Sympathy is the science of converting between multiple forms of energy through force of will ("Alar"), and is often considered a type of magic, albeit a demystified (in comparison to Naming) one as the mechanics and math are quite well understood. This changing is done through any one of at least ninety bindings (and potentially several dozen advanced bindings), such as "Motion to Light" or "Parallel Motion". A binding is cast through muttering the words and focusing. It is extremely difficult for a sympathist to maintain multiple bindings, as the mind must be split to maintain them; Kvothe can manage six, and Devi can manage eight. Sympathists may use a focus, such as pine sap  or a piece of metal , to help them concentrate and perform the bindings.
As with many practices of the University, sympathy is viewed with superstition by those who have not studied it. Those not educated in it frequently treat it as a dark art associated with demons.
Mechanics of Sympathy
By use of circular reasoning, a sympathist must convince himself that the effect he desires is real. It becomes real because he believes it is so with enough force of will to make it so. With the addition of a spoken (usually muttered) phrase, a "sympathic binding," the desired effect is achieved and things can be linked together. No link is perfect; more similar items are easier to link. For example, when Kvothe links two drabs together and moves them in parallel, he must lift the drab in his hand with the effort of moving three drabs to also move the linked drab. Kvothe describes this effect as being like a "leak aqueduct leading to a water wheel. A good sympathetic link has few leaks, and most of the energy is used."  A bad link requires considerably more force.
Things which have actually been linked before (ex. a branch which has been broken in half) work the best. Things which have conceivably been linked work quite well (ex. drabs which could have come from the same bar of iron). Items which are only similar hold a link well enough to perform useful tasks (ex. a wax or clay simulacra (a doll) of a person which bears their shape and perhaps their blood, skin, or hair), but in truth anything can be linked if one is willing to accept the additional energy needed to do work.
Sympathy also requires a source of energy. It is common for sympathists to use multiple links, one being an energy source, another the binding they wish to do work. Fire is a common source of energy, though sympathists will often use their own body as a source of energy - either through kinetic energy (moving their body to exert more work), or thermal (using their own body heat).
Sympathy comes with no rush of power or apparent evidence to the user that they have made a binding unless they make it poorly or use their body as an energy source. Done improperly, sympathy can be extremely dangerous to the use. A sympathist may use their own body heat -resulting in a cool sensation, "Binder's Chills," or in extreme cases even death- or physical strength (ex. they must exert more force than natural to lift something that has been bound to another).
If done poorly (for instance, calculation errors), there can be "slippage." Slippage is the effect of energy wasted and transferred into an unintended source with unintended results. This can be extremely dangerous. Thermal slippage may burn a person, possibly inflicting death; kinetic slippage may result in an impact upon them and has been so severe as to result in losing limbs. 
The laws of sympathy are as follows :
- The Doctrine of Correspondance: Similarity enhances sympathy.
- The Principle of Consanguinuity: A piece of a thing can represent the whole of a thing.
- The Law of Conservation: Energy cannot be destroyed nor created.
The less similar two objects are, the harder it is to perform and sustain the binding.
The following is a non-comprehensive list of the bindings of Sympathy. There are easily over one-hundred different bindings. :
- Kinetic: Used to transfer energy of motion
- Sympathetic Binding of Parallel Motion 
- First Parallel Kinetic Binding (This may be the same as the Sympathetic Binding of Parallel Motion)
- Chemical: Used to transfer chemical energy
- Chemical, Second Catalytic
- Galvanic: Used to transfer electromagnetic energy
- Binding for Linear Galvanic Attraction
- Mixed: Used to transfer one kind of energy into another.
- Capacatorial Kinetic Luminosity: "Motion to Light;" One can use the kinetic motion of an object, such as their hands, to generate light.
- Maxim of Variable Heat Transferred to Constant Motion
- The words of the sympathetic bindings are never said in the book.