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This is the first in a series of papers on an attempt to understand quantumfield theory mathematically. In this paper we shall introduce and study BV QFTalgebra and BV QFT as the proto-algebraic model of quantum field theory byexploiting Batalin-Vilkovisky quantization scheme. We shall develop a completetheory of obstruction (anomaly) to quantization of classical observables andpropose that expectation value of quantized observable is certain quantumhomotopy invariant. We shall, then, suggest a new method, bypassing Feynman'spath integrals, of computing quantum correlation functions when there is noanomaly. An exact solution for all quantum correlation functions shall bepresented provided that the number of equivalence classes of observables isfinite for each ghost numbers. Such a theory shall have its natural familyparametrized by a smooth-formal moduli space in quantum coordinates, whichnotion generalize that of flat or special coordinates in topological stringtheories and shall be interpreted as an example of quasi-isomorphism of generalQFT algebra.

Algebraic Principles of Quantum Field Theory I: Foundation and an exact solution of BV QFT