Final answer:
Igor Stravinsky's career encompassed the Russian, Neoclassical, and Serial periods, each reflecting the compositional practices and aesthetic philosophies prevalent during those times.
Step-by-step explanation:
The stylistic periods that Igor Stravinsky went through during his career as a composer include the Russian, Neoclassical, and Serial periods. Stravinsky started with the Russian period, which was characterized by nationalistic music that was typical in the post-Romantic era where composers like Stravinsky were inspired by the traditions of their own countries. Stravinsky's famous work, the Rite of Spring, caused a scandal with its avant-garde approach during this time.
After the Russian period, Stravinsky embraced the Neoclassical style, which was a return to the classical ideals and forms of the Greek arts and represented a rejection of the ornate and complex Baroque and Rococo periods. This style was characterized by clarity, order, and balance, as seen in Neoclassical art with heroes depicted in static positions, which is exemplified by Stravinsky's compositions during this time.
Lastly, Stravinsky ventured into the Serial period in his later years, experimenting with techniques that involved a series of tones in a particular order that form the basis of the composition, moving away from traditional tonal systems.