Big-bang nucleosynthesis (BBN) is the process that produced light elements in the early universe, providing a key test of the standard hot big-bang cosmology. Predictions for the abundances of deuterium (D), helium-3 (³He), helium-4 (⁴He), and lithium-7 (⁷Li) agree well with observational data, validating the standard model. These abundances are sensitive to the baryon-to-photon ratio (η), which is constrained to a range of 3.4–6.9 (95% CL). This range corresponds to a baryon density of 0.012–0.025 h⁻², where h is the Hubble constant. The abundance of ⁴He is primarily determined by the neutron-proton ratio, which is influenced by weak interactions and the expansion rate of the universe. The observed abundances of D, ³He, and ⁷Li are consistent with BBN predictions, though there is some discrepancy between ⁴He and D abundances. This discrepancy may be due to systematic errors or new physics. The CMB provides an independent measure of the baryon density, which is consistent with BBN predictions. BBN also constrains the number of relativistic neutrino species (Nν), with Nν = 3 being the standard value. Beyond the Standard Model, BBN can constrain new physics, such as the existence of additional neutrino species or new particles that affect the expansion rate. The results from BBN are crucial for understanding the early universe and testing theories beyond the Standard Model. The agreement between BBN predictions and observations supports the standard cosmological model and provides constraints on possible deviations from it.Big-bang nucleosynthesis (BBN) is the process that produced light elements in the early universe, providing a key test of the standard hot big-bang cosmology. Predictions for the abundances of deuterium (D), helium-3 (³He), helium-4 (⁴He), and lithium-7 (⁷Li) agree well with observational data, validating the standard model. These abundances are sensitive to the baryon-to-photon ratio (η), which is constrained to a range of 3.4–6.9 (95% CL). This range corresponds to a baryon density of 0.012–0.025 h⁻², where h is the Hubble constant. The abundance of ⁴He is primarily determined by the neutron-proton ratio, which is influenced by weak interactions and the expansion rate of the universe. The observed abundances of D, ³He, and ⁷Li are consistent with BBN predictions, though there is some discrepancy between ⁴He and D abundances. This discrepancy may be due to systematic errors or new physics. The CMB provides an independent measure of the baryon density, which is consistent with BBN predictions. BBN also constrains the number of relativistic neutrino species (Nν), with Nν = 3 being the standard value. Beyond the Standard Model, BBN can constrain new physics, such as the existence of additional neutrino species or new particles that affect the expansion rate. The results from BBN are crucial for understanding the early universe and testing theories beyond the Standard Model. The agreement between BBN predictions and observations supports the standard cosmological model and provides constraints on possible deviations from it.