الْحَمْدُ لِلَّهِ
All praise belongs to Allah.
Hamd is praise offered in recognition of excellence or beneficence. Madḥ can be broader: even a quality not arising from deliberate action may be admired. Shukr concerns grateful acknowledgment of a benefit received. The concepts overlap, but are not interchangeable in every context.
Example: Commending wisdom or justice illustrates praise; responding appreciatively to a particular kindness illustrates gratitude.
The prefixed lām in لِلَّهِ expresses entitlement or proper attribution: Allah is supremely deserving of praise. This does not forbid giving appropriate praise to people, whose excellences are themselves dependent upon Allah.