desert (v.)

c. 1600, transitive, "to leave, abandon," either in a good or bad sense; 1640s, in reference to military service or duty, "leave without permission;" from French déserter "cause to leave," literally "undo or sever connection," from Late Latin desertare, frequentative of Latin deserere "to abandon, to leave, forsake, give up, leave in the lurch," from de "undo" (see de-) + serere "join together, put in a row" (from PIE root *ser- (2) "to line up"). Intransitive sense of "quit (a service or post) without permission" is from 1680s. Related: Deserted; deserting.

desert (n.1)

c. 1200, "wasteland, wilderness, barren area," wooded or not, from Old French desert (12c.) "desert, wilderness, wasteland; destruction, ruin" and directly from Late Latin desertum (source of Italian diserto, Old Provençal dezert, Spanish desierto), literally "thing abandoned" (used in Vulgate to translate "wilderness"), noun use of neuter past participle of Latin deserere "forsake" (see desert (v.)).

Sense of "waterless, treeless region of considerable extent" was in Middle English and gradually became the main meaning. Classical Latin indicated this idea with deserta, plural of desertus. Commonly spelled desart in 18c., which is unetymological, but it avoids confusion with the two other senses of the word. 

Every important worker will report what life there is in him. It makes no odds into what seeming deserts the poet is born. Though all his neighbors pronounce it a Sahara, it will be a paradise to him; for the desert which we see is the result of the barrenness of our experience. [Thoreau, Journal, May 6, 1854]

desert (n.2)

c. 1300, "fact of deserving a certain treatment (for good or ill) for one's behavior," from Old French deserte "merit, recompense," noun use of past participle of deservir "be worthy to have," ultimately from Latin deservire "serve well," from de- "completely" (see de-) + servire "to serve" (see serve (v.)). Meaning "suitable reward or punishment, what one deserves" (now usually plural and with just), is from late 14c.

desert (adj.)

mid-13c., "deserted, uncultivated, waste, barren, unproductive," from Old French desert and Latin desertum (see desert (n.1)). Meaning "pertaining to or belonging to a desert" is from 1630s. Desert island, one that is uninhabited, is from c. 1600. 

Definitions of desert
desert (v.)
leave someone who needs or counts on you; leave in the lurch;
The mother deserted her children
Synonyms: abandon / forsake / desolate
desert (v.)
desert (a cause, a country or an army), often in order to join the opposing cause, country, or army;
If soldiers deserted Hitler's army, they were shot
Synonyms: defect
desert (v.)
leave behind;
the students deserted the campus after the end of exam period
desert (n.)
arid land with little or no vegetation;
desert (n.)
(usually plural) a person's deservingness of or entitlement to reward or punishment;