Here's a list of common Greek roots and their meanings which I compiled myself. Any questions, comments, corrigenda, or addenda, don't hesitate to msg me.

A note on the spelling: All these roots are spelled in the Latin way, which means C for kappa, the diphthongs AE for alpha-iota and OE for omicron-iota/omega-iota, Y for upsilon, and N for gamma-nasal. In English they might be spelled with K for kappa or simple E for either diphthong. Thus the Greek "oikia" (οικια) gives the Latin "oeconomia" and the English "economy" (formerly "oeconomy"). You see how it works.

Root              Meaning               As In
a(n)		not                   agnostic
acou		hearing               acoustic
acr		high                  acrophobia
adelph		brother               Philadelphia
aer		air                   aerodynamic
aesthes, -t	perception            anaesthesia
aeti		cause                 aetiology
agath		good                  agathodemon
agog		guide                 pedagogue
agon		contest               protagonist
agora		marketplace           agoraphobia
agr		field                 agronomy
all		other                 allophone
amph		both                  amphitheatre
ana		up                    anabolic
andr		male                  androgenous
angel		messenger             angel
angi		vessel                angiosperm
anth		flower                chrysanthemum
anthrop		mankind               anthropology
anti		against               antibody
apo		away                  apogee
arch(ae)  	beginning OR ruler    archaeology, monarch
arist		best                  aristocracy
arithm		number                arithmetic
aroma		smell                 aroma
arthr		joint                 arthroscopy
ast(e)r		star                  asterisk
athl		athlete               athlete
aut		self                  automobile
ball see bol
bapt		dip                   baptist
bar		heavy                 baritone
bas		base OR walking       basis
bathy		deep                  bathysphere
bi(o)		life                  biosphere
bibli		book                  bibliophile
bol, ball 	cast                  ballistic
brach(y)  	short                 tribrach
cac		bad                   cacophony
calyps, -t	covered               calypso
card		heart                 tachycardia
carp		fruit                 mesocarp
cata		down                  catastrophe
centr		center                centre
cephal		head                  cephalization
ch(e)ir		hand                  sthenochire
chiasm		cross                 chiasma
chlor		green                 chlorine
chord		string                chordophone
chore		dance                 choreography
chrom		colour                chromatic
chron		time                  chronoscope
chthon		ground                chthonian
chym		juice                 chyme
cin		motion                cinema
clin		tilt                  clinic
coel		hollow                coelom
cosm(et)  	world OR ordered      cosmopolitan, cosmetic
crac, crat	power                 democrat
cras		mixing                crasis
cris, crit        sift, discern         criterion
crypt		hidden                cryptography
cyan		blue                  cyanogen
cycl		circular              cyclic
dec		ten                   decathlon
dem		populus               democracy
dendr		tree                  dendrite
derm		skin                  dermatologist
di                two                   dilemma
dia		through               diagnosis
dox		opinion               orthodox
drom		racecourse            dromedary
dynam		power                 dynamo
ec(to), ex	out                   ectothermic
electr		amber OR electricity  electrum, electric
en(do)		in                    endogenous
epi		upon                  epitaph
epistem		knowledge             epistemology
epistol		letter                epistolary
eros, -t  	sex                   erotic
erg, urg  	work                  energy
erythr		red                   erythrocyte
ethn		race                  ethnic
eu		well                  euphonium
eury		broad                 eurypterid
gam		marriage              monogamy
ge		earth                 geography
gen(es), -t	birth OR type         genetic
gloss, glot	tongue                glossary, polyglot
glyph		carving               hieroglyph
gnath		jaw                   gnathometer
gnom		judgement OR aphorism gnomic
gnomon            sundial's index       gnomonic
gnos		know                  gnostic
gon		offspring OR angle    gonad, polygon
gram		written message       telegram
graph		write                 telegraph
gymn		naked                 gymnasium
gyn(aec)  	woman                 gynecology
gyr		circular motion       gyroscope
haem		blood                 hemoglobin
heli		sun                   helium
hellen		Greek                 hellenophile
helminth  	worm                  platyhelminth
hemer		day                   ephemeral
hept		seven                 heptad
hex		six                   hexad
hier		temple                hierophant
hipp		horse                 hippopotamus
hydr		water                 hydration
hygr		moisture              hygroscope
hyper		over                  hyperbaric
hypn		sleep                 hypnotic
hypo		under                 hypochondriac
ichthy		fish                  ichthyology
iod		violet                iodine
iso		equal                 isometric
itis		irritation            conjunctivitis
labyrinth  	maze                  labyrinth
leuc		white                 leucocyte
lith		stone                 lithography
log		word OR study         dialogue
lys, -z, -t	break OR loosen       analyze
macr		long                  macron
math		learning              math
meg(al)		big                   megalomania
melan		black                 melanin
mer		part                  polymer
meta		with OR after         metamorphic
met(e)r		measure               meter
micr		small                 micron
mim		imitate               pantomime
mis		hatred                misogynist
mnem, -s, -t	remember              mnemonic
mon		single                monad
mor		fool                  sohpomore
morph		form                  morphology
music		music                 music
myc		fungus                mycology
narc		numbness              narcotic
ne(o)		new                   neoplast
necr		corpse                necrophilia
neur		nerve                 neuron
nom		law                   nomic
ochr		brown                 ochre
oct		eight                 octagon
odon(t)		tooth                 pterodon
oec		home                  ecology
oen		wine                  oenology
olig		few                   oligarchy
onc		swelling              oncogene
onom(at), onym	name                  pseudonym
o(ö)		egg                   oocyte
ophthalm  	eye                   ophthalmoscope
ops, opt(ic)	sight                 optics
orex		appetite              anorexia
ornith		bird                  ornithology
orth		correct OR straight   orthography, orthorhombic
paed		child                 pedophile
palae		ancient               palaeography
pan(t)		all                   panorama
para		alongside             paranormal
parthen		virgin                parthenogenesis
path		disease               pathology
pent		five                  pentagram
peri		around                periscope
phae		gray                  phaeochrome
phaen		appear                phenomenon
phag		eat                   xylophagous
phil		love                  philanthropy
phob		fear                  homophobia
phon		sound                 phonic
phot		light                 photography
phyll		leaf                  chlorophyll
phyt		plant                 bathyphyte
pin		drink                 pinocytosis
plast		mould                 rhinoplasty
platy		flat                  platyhelminth
plex, plect	strike                apoplexy
pleth		multitude             plethora
pnoe, pneum(at)	breath                pneumonia
pod		foot                  gastropod
poeia, -sis, -t	do, make OR poem      poet
polem		war                   polemic
polis, -t  	city                  metropolis
poly		many                  polygamy
pragm		action                pragmatic
prot		first                 protozoa
pseph		voting                psephology
pseud		false                 pseudonym
psych		soul                  psychology
pyr		fire                  pyre
rhabd		rod                   rhabdomancy
rhe, rrhoe        flow                  diarrhea
rhem(at)  	word                  rhematic
rhin		nose                  rhinocerous
rhiz		root                  mycorrhiza
sarc		flesh                 sarcasm
scop		view                  endoscopy
sem		symbol                semantics
som		body                  somatic
soph		wisdom                sophistry
sperm		seed                  sperm
sphaer		sphere                ionosphere
spongi		sponge                sponge
spor		sowing                spore
sten		narrow                stenography
ster(e)		solid OR 3D           stereo
sthen		strength              sthenochire
stigm(at) 	mark OR puncture      stigmata
stom		mouth                 colostomy
strat(eg) 	army                  strategy
strob		whirl                 stroboscope
stroph, -eph,
-eps, -ept	turn OR twist         catastrophe
syn, sym          with OR together      symbiotic
tach(y)		fast                  tachyon
taph		tomb                  cenotaph
techn		craft                 technical
tect		builder               architect
tel(e)		far                   telephone
tetr		four                  tetrad
thalass, -tt	ocean                 panthalassa
thanas, -t	death                 euthanasia
thaum(at) 	miracle               thaumaturgy
the		god                   theocracy
theatr		theatre               theatre
therap		therapy               therapy
ther(i)		beast                 megatherium
therm		heat                  thermometer
thes, thet	position              thesis
tom		cut                   hysterectomy
tox(ic)		poison OR arrow       toxic
tri		three                 trigonometry
troph		nourish               atrophy
urg see erg
xanth		yellow                xanthochrome
xen		strange               xenophobe
xer		dry                   xerox
xiph(i)		sword                 xiphoid
xyl		wood                  xylophone
zo(ö)		animal                zoo
zyg		yoke OR connection    zygote
zym		fermentation          zymology

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