1. Where Mt is the magnetization at time = t, the time after the 90o pulse, Mmax is the maximum magnetization at full recovery.
At a time = one T1, the signal will recover to 63% of its initial value after the RF pulse has been applied. After two T1 times, the magnetization is at 86% of its original length. Three T1 times gives 95%. Spins are considered completely relaxed after 3-5 T1 times.
Another term that you may hear is the T1 relaxation rate. This is merely the reciprocal of the T1 time (1/T1). T1 relaxation is fastest when the motion of the nucleus (rotations and translations or "tumbling rate") matches that of the Larmor frequency. As a result, T1 relaxation is dependent on the main magnetic field strength that specifies the Larmor frequency. Higher magnetic fields are associated with longer T1 times.
T1 weighted images can be obtained using an inversion recovery sequence or by setting short TR (<750ms) and TE (<40ms) values in conventional spin echo sequences. In gradient echo sequences, T1WI can be obtained by using flip angles over 50o and setting the TE to less than 15 ms.

3. T2 Relaxation Time
T2 relaxation refers to the progressive dephasing of spinning dipoles following the 90° pulse as seen in a spin-echo sequence due to tissue-particular characteristics, primarily those that affect the rate of movement of protons, most of which are found in water molecules. This is alternatively known as spin-spin relaxation.
Immediately after the 90° pulse, all the spinning dipoles within the slice are exactly in phase. Almost immediately, they lose coherence as some spin slightly faster than the others.
This dephasing effect has been likened to the opening of a chinese fan. The result is that the Mxy component of the magnetic vector decreases exponentially as a function of the T2 time constant.

4. Factors affecting T2 relaxation
Each magnetic dipole exists in a micro environment unique to the tissue where it belongs. In all tissues, there exist tiny magnetic fields (~1mT) generated by the spinning hydrogen nuclei (protons).
T2 relaxation occurs in a varying local magnetic field when there is transfer of energy between dipoles facing parallel and antiparallel to the external magnetic field, flipping each other in opposite directions.
This rate of flipping or transfer of energy between spins or dipoles increases as the frequency of the variation of the local magnetic field approaches the Larmor frequency.
This is related to the rate of rotation and translation of the water molecule or adjacent dipoles. The dipole-dipole interaction is also increased the strength of the local field which is dependent on the proximity of the adjacent dipoles.
In pure water T2 is long, about 3-4 seconds because water molecules move considerably faster than the Larmor frequency. The rapid motion results in the T1 and T2 being about the same in pure water.

5. In solutions of macromolecules and tissues the relaxation rate is much faster, i.e., the T2 time is shorter.
This is related in part to the slower motion of protons both in macromolecules as well as water molecules attracted to the surface of the macromolecule. This slower motion is closer to the Larmor frequency.
Examples of T1 and T2 in biological tissues include: CSF, T1=1.9 seconds and T2=0.25 seconds; brain white matter, T1=0.5 seconds and T2=0.07 seconds (70 msec).
As motion and therefore the local field fluctuations decreases below the Larmor frequency in tissues and tendons, dipoles that are aligned with the main magnetic field start contributing to T2 relaxation by causing local variations in precession rate.
The resulting short T2 time causes tendons and other semi-solid tissues to appear dark on T2-weighted images. Long T2 fluids with few macromolecules such as water, urine and CSF will appear bright on T2-weighted images.

6. Loss of signal and darkness on T2-weighted images in cortical bone, teeth, calculi is primarily a result of little water (low proton density) unlike tendons and ligaments 3.
The water that is in bone, teeth and calculi would mostly be bound as to collagen and would have a very short T2 time constant and appear dark. There is also mild susceptibility differences between bone and soft tissue that could contribute to a dark appearance at interfaces, as between marrow and bone trabecula. This is seen in particular on gradient echo images.
Note: T2 relaxation is not to be confused with T2* which is a broader phenomenon and includes static magnetic field effects in addition to the tissue-characteristic T2 relaxation.

8. Repetition time (TR)
The repetition time (TR) is the time from the application of an excitation pulse to the application of the next pulse. It determines how much longitudinal magnetization recovers between each pulse. It is measured in milliseconds.