Big-bang nucleosynthesis (BBN) is a powerful probe of the early universe, based on well-understood Standard Model physics. The abundances of light elements such as deuterium (D), helium-3 (³He), helium-4 (⁴He), and lithium-7 (⁷Li) synthesized during the first three minutes after the Big Bang are in good agreement with observational data, validating the standard hot big-bang cosmology. This agreement spans nine orders of magnitude in abundance, from ⁴He/H ∼ 0.08 to ⁷Li/H ∼ 10⁻¹⁰, making BBN a stringent test of the standard model and constraints on new physics beyond it. The synthesis of light elements occurs at temperatures below 1 MeV, where weak interactions are in thermal equilibrium. The neutron-proton ratio (n/p) is determined by the neutron-proton mass difference (Q = 1.293 MeV). As the temperature drops, the neutron-proton conversion rate falls faster than the Hubble expansion rate, leading to chemical equilibrium "freeze-out" at Tfr ∼ 1 MeV. The neutron fraction at this point is sensitive to all known physical interactions. After freeze-out, neutrons decay, reducing the neutron fraction to about 1/7 by the time nuclear reactions begin. The rates of these reactions depend on the baryon density (η), which is normalized to the blackbody photon density. The allowed range for η is 3.4–6.9 (95% CL), corresponding to a baryon mass density of (2.3–4.7) × 10⁻³¹ g cm⁻³. The primordial abundance of ⁴He (Yp) is estimated to be around 0.25, while the abundances of D, ³He, and ⁷Li are much lower, with ⁷Li/H ∼ 10⁻¹⁰. The neutron lifetime (τn) is crucial for determining Yp, and recent measurements have reduced its uncertainty to τn = 885.7 ± 0.8 s. Recent observations of D in high-redshift, low-metallicity quasar absorption systems provide the first measurements of light element abundances at cosmological distances. The observed D/H values are consistent with the BBN predictions, but systematic errors remain a concern. Observations of ⁴He in metal-poor dwarf galaxies confirm that the small stellar contribution to helium is positively correlated with metal production. Li observations in metal-poor stars in the spheroid of our Galaxy suggest a primordial Li/H value of (0.59 - 4.1) × 10⁻¹⁰. BBN provides a key test of the standard cosmology, with the overlap in the η ranges spanned by theBig-bang nucleosynthesis (BBN) is a powerful probe of the early universe, based on well-understood Standard Model physics. The abundances of light elements such as deuterium (D), helium-3 (³He), helium-4 (⁴He), and lithium-7 (⁷Li) synthesized during the first three minutes after the Big Bang are in good agreement with observational data, validating the standard hot big-bang cosmology. This agreement spans nine orders of magnitude in abundance, from ⁴He/H ∼ 0.08 to ⁷Li/H ∼ 10⁻¹⁰, making BBN a stringent test of the standard model and constraints on new physics beyond it. The synthesis of light elements occurs at temperatures below 1 MeV, where weak interactions are in thermal equilibrium. The neutron-proton ratio (n/p) is determined by the neutron-proton mass difference (Q = 1.293 MeV). As the temperature drops, the neutron-proton conversion rate falls faster than the Hubble expansion rate, leading to chemical equilibrium "freeze-out" at Tfr ∼ 1 MeV. The neutron fraction at this point is sensitive to all known physical interactions. After freeze-out, neutrons decay, reducing the neutron fraction to about 1/7 by the time nuclear reactions begin. The rates of these reactions depend on the baryon density (η), which is normalized to the blackbody photon density. The allowed range for η is 3.4–6.9 (95% CL), corresponding to a baryon mass density of (2.3–4.7) × 10⁻³¹ g cm⁻³. The primordial abundance of ⁴He (Yp) is estimated to be around 0.25, while the abundances of D, ³He, and ⁷Li are much lower, with ⁷Li/H ∼ 10⁻¹⁰. The neutron lifetime (τn) is crucial for determining Yp, and recent measurements have reduced its uncertainty to τn = 885.7 ± 0.8 s. Recent observations of D in high-redshift, low-metallicity quasar absorption systems provide the first measurements of light element abundances at cosmological distances. The observed D/H values are consistent with the BBN predictions, but systematic errors remain a concern. Observations of ⁴He in metal-poor dwarf galaxies confirm that the small stellar contribution to helium is positively correlated with metal production. Li observations in metal-poor stars in the spheroid of our Galaxy suggest a primordial Li/H value of (0.59 - 4.1) × 10⁻¹⁰. BBN provides a key test of the standard cosmology, with the overlap in the η ranges spanned by the