Short answers, pulled from the story.
Inorganic chemistry deals with the synthesis and behavior of inorganic and organometallic compounds, covering chemical compounds that are not carbon-based. It has applications across the chemical industry, including catalysis, materials science, pigments, surfactants, coatings, medications, fuels, and agriculture.
Inorganic chemistry covers compounds that are not carbon-based, while organic chemistry studies carbon-based compounds. The distinction is far from absolute, because the two overlap heavily in the subdiscipline of organometallic chemistry, which involves metal-carbon bonds.
The subdivisions of inorganic chemistry include organometallic chemistry, cluster chemistry, bioinorganic chemistry, and materials chemistry and solid state chemistry. Organometallic chemistry involves metal-carbon bonds, cluster chemistry involves several metals bound by metal-metal bonds or bridging ligands, and bioinorganic chemistry involves biomolecules that contain metals.
Carl Bosch and Fritz Haber discovered a practical synthesis of ammonia using iron catalysts in the early 1900s. This discovery deeply impacted mankind and demonstrated the significance of inorganic chemical synthesis. The ammonia is produced through the Haber process.
Inorganic compounds are characterized using X-ray crystallography for three-dimensional structure determination and various forms of spectroscopy, including ultraviolet-visible, NMR, and infrared spectroscopy. Other methods include Mossbauer spectroscopy, electron-spin resonance, and electrochemistry techniques such as cyclic voltammetry.
Many inorganic compounds are magnetic or colored, unlike most organic compounds, and these properties provide information on bonding and structure. For example, most copper(II) compounds are paramagnetic, but one copper acetate complex is almost diamagnetic below room temperature due to magnetic coupling between pairs of copper sites.