Both molecules and all types of condensed matter (solids etc.) are created by means of the Coulomb diagonal and nondiagonal (covalent) bonds. However, the band bonds of free electrons are typical for metals. The quantum statistics describes increasing competition of the band and covalent bonds with a motion down the Mendeleev table: from almost band (nontransition) metals to transition metals and alloys with a changing filling of $nd$- ($n \geq 3$) and $mf$- ($m \geq 4$) ionic shells. The Bogolyubov’s Green functions’ method in the band fermions ($f_{r\sigma}$) representations at the sites $r$ with the spin $\sigma$ and in the representation of the many-electron operator spinors (MEOS) $D_{r}(S_{r}, L_{r})$ of ionic shells with the spin $S_{r}$ and orbital moment $L_{r}$ gives the spectra of band fermions and chemical (covalent) bonds’ fluctuations (CBF). Almost band (Cu–Ni like) one-phase (f.c.c.) alloys and polymorphic ones (Fe alloys) with dominating the covalent ionic and spin (exchange) bonds are compared. The Fourier expansion of MEOS ($D_{k}$) and fermions $f_{k}$ extracts the CBF branches $E_{k}$, band $\tilde{\varepsilon_{k}}$, magnon and other branches from pair interactions. Hence, the crossing whith CBF near the Fermi surfaces $\varepsilon_{F}(k_{F})$ leads to the $ ilde{\varepsilon_k}$ anomalies and density of states (DOS($E$)) singularities. The defects of elastic modulus, Invar effects near the b.c.c.–f.c.c. phase transitions are calculated. The magnetic order type (ferromagnetic (FM) or antiferromagnetic (AFM), clusters, etc.) is determined by bonding or antibonding covalent (and exchange) interactions. The theory describes the reduction of local symmetry at the introduction of light impurities (as C) by a form of the internal friction peak $Q^{-1}(T)$ as a function of temperature $T$. The hybridization of $ms–nd$-electrons through the Fe$^{57}$ covalent bonds expresses hyperfine fields $H_{F}$ through the mean spins $S_{T}$ of the metal matrix, and the isomeric displacement of $\gamma$-lines $R_{c}$ through the CBF as a function of $T$ and alloy concentration.