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In this paper we generalize the method used to prove the Prime Number Theorem to deal with finite fields, and prove the following theorem: $$\pi \left(x\right)=\frac{q}{q-1}\frac{x}{{log}_{q}x}+\frac{q}{{(q-1)}^2}\frac{x}{{log}_q^{2}x}+O\left(\frac{x}{{log}_q^{3}x}\right),x=q^n\to \infty$$ where $\pi \left(x\right)$ denotes the number of monic irreducible polynomials in $F_q\left[t\right]$ with norm $\le x$.