  Cygnus X-3 (Cyg X-3) is a well-known microquasar producing variable emission
at all wavelengths. Cyg X-3 is a prominent X-ray binary producing relativistic
jets, and studying its high energy emission is crucial for the understanding of
the fundamental acceleration processes in accreting compact objects. Aims. Our
goal is to study extreme particle acceleration and {\gamma}-ray production
above 100 MeV during special spectral states of Cyg X- 3 usually characterized
by a low hard X-ray flux and enhanced soft X-ray states. We observed Cyg X-3
with the AGILE satellite in extended time intervals from 2009 Jun.-Jul., and
2009 Nov.-2010 Jul. We report here the results of the AGILE {\gamma}-ray
monitoring of Cyg X-3 as well as the results from extensive multiwavelength
campaigns involving radio (RATAN-600, AMI-LA and Mets\"{a}hovi Radio
Observatories) and X-ray monitoring data (XTE and Swift). We detect a series of
repeated {\gamma}-ray flaring activity from Cyg X-3 that correlate with the
soft X-ray states and episodes of decreasing or non-detectable hard X-ray
emission. Furthermore, we detect {\gamma}-ray enhanced emission that tends to
be associated with radio flares greater than 1 Jy at 15 GHz, confirming a trend
already detected in previous observations. The source remained active above 100
MeV for an extended period of time (almost 1.5 months in 2009 Jun.-Jul. and 1
month in 2010 May). We study in detail the short timescale {\gamma}-ray flares
that occurred before or near the radio peaks. Our results confirm the transient
nature of the extreme particle acceleration from the microquasar Cyg X-3. A
series of repeated {\gamma}-ray flares shows correlations with radio and X-ray
emission confirming a well established trend of emission. We compare our
results with Fermi-LAT and MAGIC TeV observations of Cyg X-3.
