Stratosphere - The thermal atmospheric region of the atmosphere between the troposphere and the mesosphere. The lower boundary of the stratospheric region is marked by the tropopause and begins at approximately 13 kilometers; however, this altitude of the troposphere depends on latitude. The upper limit of the stratosphere is marked by the stratopause at approximately 50 kilometers. The stratosphere is characterized by relatively stable temperatures (between -80 and -50 degrees Celsius) in the lower regions, and begins warming near 20 kilometers, reaching its maximum temperature of approximately 0 degree Celsius at the stratopause. Stratospheric chemistry is of particular interest to scientists because ozone, the principal substance that shields the earth from incoming solar ultraviolet radiation, is found in the stratosphere. It should also be noted that wind currents in the stratosphere are primarily horizontal in nature.
[Journal of the Atmospheric Sciences; v50; 3928-38; 1993.]
[Nature; v370; 429-34; 1994.] 
Atmospheric Chemistry Glossary

That region of the Earth's atmosphere between the troposphere and the mesosphere. It begins at an altitude of temperature minimum at approximately 13 km and defines a layer of increasing temperature up to about 30 km.

Region of the atmosphere between the troposphere and mesosphere, having a lower boundary of approximately 8 km at the poles to 15 km at the equator and an upper boundary of approximately 50 km. Depending upon latitude and season, the temperature in the lower stratosphere can increase, be isothermal, or even decrease with altitude, but the temperature in the upper stratosphere generally increases with height due to absorption of solar radiation by ozone.
NASA Earth Observatory

Stratosphere: the region of the atmosphere above the troposphere

The stratosphere extends from about 10km to about 50km in altitude. Commercial airlines fly in the lower stratosphere. The stratosphere gets warmer at higher altitudes. In fact, this warming is caused by ozone absorbing ultraviolet radiation. Warm air remains in the upper stratosphere, and cool air remains lower, so there is much less vertical mixing in this region than in the troposphere.

The layer of the atmosphere above the troposphere and below the mesosphere (between 10 km and 50 km), generally characterized by an increase in temperature with height.
WRCC Climate and Weather Terms Glossary