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It is shown that the ground-state and the lowest excited-states oftwo-dimensional electron system (2DES), with ion jellium background, correspondto partial crystal-like (with the period $L_{x}^{\square}=\sqrt{2 m \pi}\ell_{0}$) correlation order among $N$ electrons of the main region (MR; $L_{x}\times L_{y}$). Many-body variational ground-state wave function of 2DES ispresented at the fractional and the integral filling factors $\nu=1/m$;$m=2\ell+1$ and $\ell=0, 1, 2,...$. The ground-state manifests the brokensymmetry liquid-crystal state with 2DES density that is periodic along the $y-$direction, with the period $L_{x}^{\square}/m$, and independent of $x$. At$m=3, 5$, the ground-state has essentially lower energy per electron than theLaughlin, uniform liquid, ground-state; the same holds at $m=1$. At $m \geq 3$,the compound form of the many-body ground-state wave function leads to thecompound structure of each electron within the main strip (MS; $L_{x}^{\square}\times L_{y}$). Obtained compound exciton and compound spin-exciton states showfinite excitation gaps. The excited compound electron (hole) is composed,within MS, from $m$ strongly correlated quasielectrons (quasiholes) of thetotal charge $e/m$ ($-e/m$) each. The activation gap is obtained: it is givenby the excitation gap of relevant compound exciton, at $m \geq 3$, and by thegap of pertinent compound spin-exciton, at $m=1$. Quantized Hall conductance$\sigma_{H}=e^{2}/(2 m \pi \hbar)$ is obtained. The theory is in good agreementwith experiments.

Fractionally Quantized Hall Effect: Liquid-Crystal Ground-State and it Excitations