[en] My lectures on the effective field theory for heavy quarks, an expansion around the static limit, concentrate on the motivation and formulation of HQET, its renormalization and discretization. This provides the basis for understanding that and how this effective theory can be formulated fully non-perturbatively in the QCD coupling, while by the very nature of an effective field theory, it is perturbative in the expansion parameter 1/m. After the couplings in the effective theory have been determined, the result at a certain order in 1/m is unique up to higher order terms in 1/m. In particular the continuum limit of the lattice regularized theory exists and leaves no trace of how it was regularized. In other words, the theory yields an asymptotic expansion of the QCD observables in 1/m - as usual in a quantum field theory modified by powers of logarithms. None of these properties has been shown rigorously (e.g. to all orders in perturbation theory) but perturbative computations and recently also non-perturbative lattice results give strong support to this ''standard wisdom''. A subtle issue is that a theoretically consistent formulation of the theory is only possible through a non-perturbative matching of its parameters with QCD at finite values of 1/m. As a consequence one finds immediately that the splitting of a result for a certain observable into, for example, lowest order and first order is ambiguous. Depending on how the matching between effective theory and QCD is done, a first order contribution may vanish and appear instead in the lowest order. For example, the often cited phenomenological HQET parameters anti Λ and λ₁ lack a unique non-perturbative definition. But this does not affect the precision of the asymptotic expansion in 1/m. The final result for an observable is correct up to order (1/m)ⁿ⁺¹ if the theory was treated including (1/m)ⁿ terms. Clearly, the weakest point of HQET is that it intrinsically is an expansion. In practise, carrying it out non-perturbatively beyond the order 1/m will be very difficult. In this context two observations are relevant. First, the expansion parameter for HQET applied to B-physics is Λ_QCD/m_b ∝ 1/(r₀m_b)=1/10 and indeed recent computations of 1/m_b corrections showed them to be very small. Second, since HQET yields the asymptotic expansion of QCD, it becomes more and more accurate the larger the mass is. It can therefore be used to constrain the large mass behavior of QCD computations done at finite, varying, quark masses. At some point, computers and computational strategies will be sufficient to simulate with lattice spacings which are small enough for a relativistic b-quark. One would then like to understand the full mass-behavior of observables and a combination of HQET and relativistic QCD will again be most useful. Already now, there is a strategy (de Divitiis et al. (2003), de Divitiis et al. (2003), Guazzini et al. (2008)), which, in its final version combines HQET and QCD in such a manner. For a short review of this aspect I refer to (Tantalo, 2008). (orig.)