(DEPTH) A sequence with multiple RF pulses to enable acquiring data from only selected regions.
See Depth Pulses, Volume Selective Excitation, Depth Resolved Spectroscopy.

Spoiled gradient echo sequences use a spoiler gradient on the slice select axis during the end module to destroy any remaining transverse magnetization after the readout gradient, which is the case for short repetition times.
As a result, only z-magnetization remains during a subsequent excitation. This types of sequences use semi-random changes in the phase of radio frequency pulses to produce a spatially independent phase shift.
Companies use different acronyms to describe certain techniques.

Different terms for these gradient echo pulse sequences:
CE-FFE-T1 Contrast Enhanced Fast Field Echo with T1 Weighting,
GFE Gradient Field Echo,
FLASH Fast Low Angle Shot,
PS Partial Saturation,
RF spoiled FAST RF Spoiled Fourier Acquired Steady State Technique,
RSSARGE Radio Frequency Spoiled Steady State Acquisition Rewound Gradient Echo
S-GRE Spoiled Gradient Echo,
SHORT Short Repetition Techniques,
SPGR Spoiled Gradient Recalled (spoiled GRASS),
STAGE T1W T1 weighted Small Tip Angle Gradient Echo,
T1-FAST T1 weighted Fourier Acquired Steady State Technique,
T1-FFE T1 weighted Fast Field Echo.
In this context, 'contrast enhanced' refers to the pulse sequence, it does not mean enhancement with a contrast agent.

A surface coil is essentially a loop of conducting material, such as copper tubing. The in-bore solenoidal sending coil is used as the transmitter of RF energy. This type of receiver coil is placed directly on or over the region of interest for increased magnetic sensitivity. The loop may form various shapes and be bent slightly to conform to the imaged body part. Surface coils have a good SNR for tissues adjacent to the coil and because the signal decrease with the distance, an eligibility homogeneity correction will equalize this over the field of view. A rule of thumb for surface coils is that the sensitivity decreases appreciably beyond a distance equal to the diameter of the coil.
The positioning of the coil is an important determinant of performance. As only the region close to the surface coil will contribute to the signal, there is an improvement in the SNR for these regions, compared to the use of receiver coils that surround the appropriate part of the body. These coils are specifically designed for localized body regions, and provide improved signal to noise ratios by limiting the spatial extent of the excitation or reception.

See also the related poll result: '3rd party coils are better than the original manufacturer coils'

The T1 relaxation time (also called spin lattice or longitudinal relaxation time), is a biological parameter that is used in MRIs to distinguish between tissue types. This tissue-specific time constant for protons, is a measure of the time taken to realign with the external magnetic field. The T1 constant will indicate how quickly the spinning nuclei will emit their absorbed RF into the surrounding tissue.
As the high-energy nuclei relax and realign, they emit energy which is recorded to provide information about their environment. The realignment with the magnetic field is termed longitudinal relaxation and the time in milliseconds required for a certain percentage of the tissue nuclei to realign is termed 'Time 1' or T1. Starting from zero magnetization in the z direction, the z magnetization will grow after excitation from zero to a value of about 63% of its final value in a time of T1. This is the basic of T1 weighted images.
The T1 time is a contrast determining tissue parameter. Due to the slow molecular motion of fat nuclei, longitudinal relaxation occurs rather rapidly and longitudinal magnetization is regained quickly. The net magnetic vector realigns with B0 leading to a short T1 time for fat.
Water is not as efficient as fat in T1 recovery due to the high mobility of the water molecules. Water nuclei do not give up their energy to the lattice (surrounding tissue) as quickly as fat, and therefore take longer to regain longitudinal magnetization, resulting in a long T1 time.

See also T1 Weighted Image, T1 Relaxation, T2 Weighted Image, and Magnetic Resonance Imaging MRI.

(TOF) The time of flight angiography is used for the imaging of vessels. Usually the sequence type is a gradient echo sequences with short TR, acquired with slices perpendicular to the direction of blood flow.
The source of diverse flow effects is the difference between the unsaturated and presaturated spins and creates a bright vascular image without the invasive use of contrast media. Flowing blood moves unsaturated spins from outside the slice into the imaging plane. These completely relaxed spins have full equilibrium magnetization and produce (when entering the imaging plane) a much higher signal than stationary spins if a gradient echo sequence is generated. This flow related enhancement is also referred to as entry slice phenomenon, or inflow enhancement.
Performing a presaturation slab on one side parallel to the slice can selectively destroy the MR signal from the in-flowing blood from this side of the slice. This allows the technique to be flow direction sensitive and to separate arteriograms or venograms. When the local magnetization of moving blood is selectively altered in a region, e.g. by selective excitation, it carries the altered magnetization with it when it moves, thus tagging the selected region for times on the order of the relaxation times.
For maximum flow signal, a complete new part of blood has to enter the slice every repetition (TR) period, which makes time of flight angiography sensitive to flow-velocity. The choice of TR and slice thickness should be appropriate to the expected flow-velocities because even small changes in slice thickness influences the performance of the TOF sequence. The use of sequential 2 dimensional Fourier transformation (2DFT) slices, 3DFT slabs, or multiple 3D slabs (chunks) are depending on the coverage required and the range of flow-velocities.
3D TOF MRA is routinely used for evaluating the Circle of Willis.

See also Magnetic Resonance Angiography and Contrast Enhanced Magnetic Resonance Angiography.