Several Greek words are translated to the English word "world".

A. Kosmos (2889)
1] an apt and harmonious arrangement or constitution, order, government
2] ornament, decoration, adornment, i.e. the arrangement of the stars, 'the heavenly hosts', as the ornament of the heavens.
3] the world, the universe
4] the circle of the earth, the earth
5] the inhabitants of the earth, men, the human family
6] the ungodly multitude; the whole mass of men alienated from God, and therefore hostile to the cause of Christ
7] world affairs, the aggregate of things earthly
   7.a] the whole circle of earthly goods, endowments riches, advantages, pleasures, etc, which although hollow and frail and
          fleeting, stir desire, seduce from God and are obstacles to the cause of Christ
8] any aggregate or general collection of particulars of any sort
   8.a] the Gentiles as contrasted to the Jews (Rom. 11:12 etc)
   8.b] of believers only, John 1:29; 3:16; 3:17; 6:33; 12:47 1 Cor. 4:9; 2 Cor. 5:19
derivation: probably from the base of (2865)
http://bible1.crosswalk.com/Lexicons/Greek/grk.cgi?number=2889&version=kjv

(2865)
1] to care for, take care of, provide for
2] to take up or carry away in order to care for and preserve
3] to carry away, bear off
4] to carry, bear, bring to, to carry away for one's self, to carry off what is one's own, to bring back
   4.a] to receive, obtain: the promised blessing
   4.b] to receive what was previously one's own, to get back, receive back, recover
derivation: from a primary komeo (to tend, i.e. take care of)
http://bible1.crosswalk.com/Lexicons/Greek/grk.cgi?number=2865&version=kjv

B. Aion (165)
1] for ever, an unbroken age, perpetuity of time, eternity
2] the worlds, universe
3] period of time, age
derivation: from the same as (104)
http://bible1.crosswalk.com/Lexicons/Greek/grk.cgi?number=165&version=kjv

(104)
1] perpetually, incessantly
2] invariably, at any and every time: when according to the circumstances something is or ought to be done again
derivation: from an obsolete primary noun (apparently meaning continued duration)
http://bible1.crosswalk.com/Lexicons/Greek/grk.cgi?number=104&version=kjv

C. Oikoumene (3625)
1] the inhabited earth
   1.a] the portion of the earth inhabited by the Greeks, in distinction from the lands of the barbarians
   1.b] the Roman empire, all the subjects of the empire
   1.c] the whole inhabited earth, the world
   1.d] the inhabitants of the earth, men
2] the universe, the world
derivation: feminine participle present passive of (3611) (as noun, by implication of (1093))
http://bible1.crosswalk.com/Lexicons/Greek/grk.cgi?number=3625&version=kjv

(3611)
1] to dwell in
derivation: from (3624)
http://bible1.crosswalk.com/Lexicons/Greek/grk.cgi?number=3611&version=kjv

(3624)
1] a house
   1.a] an inhabited house, home
   1.b]. any building whatever
       1.b.1] of a palace
       1.b.2] the house of God, the tabernacle
   1.c] any dwelling place
       1.c.1] of the human body as the abode of demons that possess it
       1.c.2] of tents, and huts, and later, of the nests, stalls, lairs, of animals
       1.c.3] the place where one has fixed his residence, one's settled abode, domicile
2] the inmates of a house, all the persons forming one family, a household
   2.a] the family of God, of the Christian Church, of the church of the Old and New Testaments
3] stock, family, descendants of one
derivation: of uncertain affinity
http://bible1.crosswalk.com/Lexicons/Greek/grk.cgi?number=3624&version=kjv

(1093)
1] arable land
2] the ground, the earth as a standing place
3] the main land as opposed to the sea or water
4] the earth as a whole
   4.a] the earth as opposed to the heavens
   4.b] the inhabited earth, the abode of men and animals
5] a country, land enclosed within fixed boundaries, a tract of land, territory, region
derivation: contracted from a root word
http://bible1.crosswalk.com/Lexicons/Greek/grk.cgi?number=1093&version=kjv

Each occurrence of this word in This Good Riddle:

012-a
The devil taketh him up into an high mountain, sheweth him all the kingdoms of the world, and said unto him, All the glory of them will I give thee, if thou wilt worship me.

Matthew 4:8 Again, the devil taketh him up into an exceeding high mountain, and sheweth him all the kingdoms of the >world  (2889)<, and the glory of them;
Luke 4:5 And the devil, taking him up into an high mountain, shewed unto him all the kingdoms of the >world (3625)< in a moment of time.