Cancelling Fields. The most basic skill one learns is to create a gravitational field to cancel out the Earth's. This is easy because the Earth's field is constant in small areas. The most one can accomplish with this is allowing objects to hover and float, motionless. However, once you apply this to cancelling other people's fields as they're creating them, the complexity of the skill is directly proportional to the field your opponent has created.
Linear Fields. This skill involves moving objects in straight lines. It's also fairly easy because you only need to create constant fields to use it. The difficulty increases with larger objects. Almost everyone is capable of this, especially for small objects.
Rotational Fields. This skill is an extension of linear fields, involving rotating objects. This is much harder because you either have to apply a field very precisely on one corner of the object, or you have to create a non constant field to create rotational forces. This is considered the end of high school level knowledge. Anyone who did well in high school is likely capable of this, especially for small objects, but it's also common to find people who can't do it.
Theoretics. Theoretics is the theoretical study of gravitational fields. It is mostly just mathematical physics and required no physical skill to excel in. Despite this, it's one of the most important fields, as breakthroughs in theoretics often lead to to better understanding of how to actually apply physical skill. It's often over looked in popular culture.
Biological Manipulation involves telekinesis inside living tissue or even inside cells to help repair wounds (although it can also be used to harm). This requires great dexterity and precision with very tiny and weak fields, in depth knowledge of how cells and living tissue work, and surgical ability. The ability to visualize is highly coveted, because experienced individuals may be able to perform non invasive surgeries for simple problems. This skill would require the same level of training and difficulty as a human neurosurgeon to develop.
Celestial-Scale Fields. This area involves the study and creation of celestial objects, especially small planets. At its simplest, it may involve deflection asteroids or changing the orbit of planets. At its highest level, it involves creating planets and for the especially gifted, stars, and is considered one of the most difficult areas of study due to its high energy costs, and the fact that it strays into relativistic fields with equivalent compactness parameters up to 0.01. At any given time there are only a couple people capable of it. Suki Taniyama is considered the leading expert in the field, and for many years ran a specialized school for the best and brightest to learn how to shape space. His work is now continued by Iman Almaz.
Biomechanics is a relatively new field, involving connecting living tissue to the mechanical. It relies less on gravity control and more on the development of materials allowing for electrical signals to travel from nerves to wires and vice versa. It was largely pioneered by Mikhail Kusnetsov and Ari Taniyama for Earth life, however on Alpha Centauri massive leaps had already been made due to the nature of life being inherently more mechanical.
Time Bending. While the name "Time Bending" is colloquial, this is the use of gravitational fields that have an equivalent compactness parameter greater than 0.1. This is illegal, as the amount of knowledge and energy required to safely execute any such field is considered impossible for most people, and even a small accident can have horrific effects. The hat lady was the first to begin exploring this field, to disastrous effects, and it wasn't until Ari Taniyama that major progress was made. He was largely crucified for his work due to past accidents.
Psychics. The existence of this is disputed. While it's known that putting small fields in the brain can effect neurons, as it would any other cell, and influence behaviors, the concept of "reading minds" or "mind control" has not been proven. There have been claims of significant results, but most of these experiments were not able to be replicated. The hat lady's work was perhaps the closest ever gotten. She was researching a way to stimulate the senses to induce illusions that change time and location, in a strange combination of pseudo science and time bending. Later Mikhail Kusnetsov discovers that she succeeded, though at a heavy cost.
