Bound states in the continuum (BICs) are zero-width (infinite lifetime) trapped eigenmodes that remain conf ined in the system even though they coexist with a continuum of extended states. The resulting high-frequency resonances may have significant applications in photonic integrated circuits, filtering, sensing, and laser. In this paper, we demonstrate that a simple design based on a photonic triple-stub cavity can display both Fabry-Pérot (FP) and Friedrich-Wintgen (FW) BICs, and their occurrence is very dependent on the way the cavity is attached to the outside medium by one or two ports. We first consider a symmetric cavity where a stub of length d3 is surrounded by two stubs of length d2, and all stubs are separated by segments of length d1. When the cavity is inserted between two ports, we demonstrate theoretically and validate experimentally the existence of symmetric BICs (S-BIC) and antisymmetric BICs (AS-BIC) of FP type under commensurability conditions between the lengths d1, d2,andd3. The S-BICs and AS-BICs may cross each other, giving rise to a doubly degenerate BIC. By breaking the symmetry of the cavity, AS-BICs and S-BICs can couple together and realize a FW-type BIC where one resonance remains with zero width while the other broadens into a bright mode. By considering two additional configurations where the triple-stub cavity is attached with one or two ports from only one side, additional BICs can be induced inside the structure. By slightly detuning from the BIC condition, the latter transforms into either an electromagnetic-induced transparency/reflection or Fano resonance. Finally, such a triple-stub cavity can be designed to realize near-perfect absorption for some frequencies. All the analytical results, obtained from the Green’s function method, have been confirmed experimentally in the radiofrequency domain using coaxial cables.