The core or center part of an atom, which contains protons having a positive charge and neutrons having no electrical charge, except in the common isotope of hydrogen, where the nucleus is a single proton.

Precession is a wobbling motion that occurs when a spinning object is the subject of an external force. Relevant to MRI, the proton of a hydrogen nucleus spins around its axis giving it an angular moment (quantum mechanics). Through the protons positive charge and its spin it generates a magnetic field and gets a magnetic dipole moment (MDM) parallel to the rotation axis. If placed in a magnetic field the magnetic dipole moment will precess about the direction of the magnetic field with an angular frequency (Larmor frequency). The Larmor equation dictates that the frequency of the precession at higher field strengths is higher.

(RF) Radio frequency refers to that portion of the electromagnetic spectrum in which electromagnetic waves can be generated by alternating current fed to an antenna.
The RF pulses used in MRI are commonly in the 1-100 megahertz range, and their effect upon a body is potential heating of tissues and foreign bodies, such as metallic implants, mainly at the surface.
This is a principal area of concern for MRI safety limits caused by absorption (see specific absorption rate) of the applied pulses of RF energy.

The higher the frequency, the larger will be the amount of heat developed.
The more ionic the biochemical environment in the tissue, the more energy that will be deposited as heat.
This effect is well known for homogeneous model systems, but the complex structure of various human tissues makes detailed theoretical calculations very difficult, if not impossible. By scanning problems, it is important to verify the transmission frequency. If the RF transmitted into the patient was, e.g. 5000 Hz lower than the resonance frequency of the protons, no protons was excited, and no signal returns.

The relaxation effect is the transition of an atom or molecule from a higher energy level to a lower one. The return of the excited proton from the high energy to the low energy level is associated with the loss of energy to the surrounding tissue. The T1 and T2 relaxation times define the way that the protons return to their resting levels after the initial radio frequency (RF) pulse. The T1 and T2 relaxation rates have an effect of the signal to noise ratio (SNR) of MR images.
The relaxation process is a result of both T1 and T2, and can be controlled by the dependency of one of the two biological parameters T1 and T2 in the recorded signal. A T1 weighted spin echo sequence is based on a short repetition time (TR) and a change of it will affect the acquisition time and the T1 weighting of the image. Increased TR results in improved SNR caused by longer recovering time for the longitudinal magnetization. Increased TE improves the T2 weighting, combined with a long TR (of several T1 times) to minimize the T1 effect.

For the wide uses of NMR spectroscopy (from mineralogy to medicine) there is a variety of different spectroscopic imaging techniques available.
A short listing of the most frequent variations: