The rotationally resolved spectrum of a fundamental band of hydrogen fluoride tetramer has been recorded using a pulsed slit-jet, diode laser spectrometer. The band has a parallel rotational structure and is assigned as the H-F out-of-plane libration fundamental with A(u) symmetry. Ninety-five ground state combination differences were fit to a symmetric top Hamiltonian to give the following ground state rotational constants: B " = 0.132 081(7) cm(-1), D-J' = 7.1(7) x 10(-7) cm(-1), D-JK' = -9(2) x 10(-7) cm(-1), H-JJJ' = 6(2) x 10(-10) cm(-1), H-JJK' = 9(7) x 10(-10) cm(-1), H-JKK' = -1.3(8) x 10(-10) cm(-1). A total of 190 transitions were fit to determine the upper state spectroscopic constants: v(4) = 714.7849(1) cm(-1), B " = 0.129 634(5) cm(-1), Delta(C-B) = 0.001 344 cm(-1), D-J' = 6.4(5) x 10(-7) cm(-1), D-JK' = -4.5(6) x 10(-7) cm(-1), Delta D-K = 2.92(8) x 10(-6) cm(-1), H-JJJ' = 3(1) x 10(-10) cm(-1), H-JKK' = -1.55(6) x 10(-8) cm(-1); Delta H-KKK = -4.65(6)x10(-8) cm(-1). Furthermore, a perpendicular band centered at 752.7 cm(-1) was observed. The band has a rotational line spacing that gives an approximate B " value of 0.132 cm(-1); it has been assigned as the E-u symmetry, H-F in-plane libration fundamental of the HF tetramer. Finally, a parallel band was observed at 741.0 cm(-1) with B " = 0.076 cm(-1) and has been assigned as the A " symmetry, H-F out-of-plane libration fundamental of the HF pentamer. Structural parameters and harmonic vibrational frequencies are estimated from first-principles, correlated MP2 and CCSD(T) calculations. These are the largest calculations performed to date for this system with respect to both orbital basis set and level of electron correlation. The CCSD(T) harmonic frequencies are, in particular, the first reported for the tetramer at this level of theory. Based on our results, we suggest "best estimates" of R-FF = 2.51 Angstrom, r(HF) = 0.947 Angstrom, and theta(HFF) = 9.7 degrees for the structural parameters and a range for D-e of 27.4 to 28.1 kcal/mol (D-0 = 19.7 to 20.4 kcal/mol) for the parameters and for the energy of the tetramer dissociating into four monomers.