A newly discovered family of high-Tc Fe-based superconductors, AeAFe4As4 (Ae = Ca, Sr, Eu and A = K, Rb, Cs), offers further opportunities to understand unconventional superconductivity in these materials. In this paper, we report on the superconducting and magnetic properties of CaKFe4As4, studied using muon spectroscopy. Zero field muon-spin-relaxation studies carried out on the CaKFe4As4 superconductor do not show any detectable magnetic anomaly at Tc or below, implying that time-reversal-symmetry is preserved in the superconducting ground state. The temperature dependence of the superfluid density of CaKFe4As4 is found to be compatible with a two-gap s+s-wave model with gap values of 8.6(4) and 2.5(3) meV, similar to the other Fe-based superconductors. The presence of two superconducting energy gaps is consistent with theoretical and other experimental studies on this material. The value of the penetration depth at T = 0 K has been determined as 289 (22) Recent years have witnessed huge research interest in Fe-based superconductors not only due to higher superconducting transition temperature, T c , but also because of the unconventional superconducting properties and interplay with various electronic ground states, such as nematic phase, magnetism [1][2][3][4][5]. This family has a diverse range of structures all containing a common Fe 2 An 2 (An = P, As, Se, Te) layer, analogous to the CuO 2 layers in high-T c cuprates [6]. A e AFe 4 As 4 (A e = Ca, Sr, Eu and A = K, Rb, Cs) materials, discovered in 2016, are the new family of Fe-based superconductors with T c of ≈ 31−36 K [7]. Until now, only a few experimental studies have been performed which show that this new family of superconductors is structurally identical to CaFe 2 As 2 , with the A e and A sites forming alternating planes along the crystallographic c-axis, separated by FeAs layers [7]. Unlike other Fe-based superconductors, A e AFe 4 As 4 does not show any structural phase transition below room temperature [8]. However, Eu-containing A e AFe 4 As 4 show a magnetic transition at ≈ 15 K [9,10]. Along with high T c values, the A e AFe 4 As 4 family also show a very high upper critical field (≈ 92 T for CaKFe 4 As 4 ) [11], similar to the optimally doped (Ba,K)Fe 2 As 2 [12] which is well above the Pauli paramagnetic limit H p (0) = 1.86 * T c for weak-coupling BCS superconductors. Measurements of the London penetration depth λ(T ) using a Tunneldiode resonator (TDR) and tunneling conductance from a Scanning tunneling microscope (STM) spectroscopy show two nodeless gaps in CaKFe 4 As 4 with a larger gap of between 6-9 meV and a smaller gap of between 1-4 meV [13]. High-resolution angle-resolved photoemission spectroscopy (ARPES) measurements and density functional theory (DFT) calculations support multi-band superconductivity in CaKFe 4 As 4 , in which Cooper pairs form in the electron and the hole bands interacting via a dominant interband repulsive interaction enhanced by Fermi surface (FS) nesting [14]. Other thermodynamic and transport measurem...